In 1962:
- "China invited Pakistan to invade India (as China attacked India)."
This claim is unverifiable - I could find no documentation that China, in 1962, invited Pakistan to jointly invade India. However, Pakistan did once consider a plan to ally with China to jointly invade India:
President Ayub Khan had held a series of meetings with his senior military commanders in the spring of 1962 to consider a "grand strategy" to force India to cede Kashmir to Pakistan ... According to Mullik's report, the field marshal believed "the only solution lay in Pakistan and China forging a grand alliance against the common enemy, India. His strategy would be that while Chinese guerillas would attack India from the north and the east and keep Indian forces heavily engaged, Pakistan would make an onslaught from the west. To make this strategy possible Ayub was willing to go to any length to court China." (Ref. 1, Page 90)
Ayub Khan also dropped hints to the US that some in Pakistan wanted to ally with China if the US couldn't resolve the Kashmir issue:
Pakistan’s people were getting fed up. This is why they sometimes talked of working more closely with China, though they didn’t want China to come in. What then did Pakistan want of China, President Kennedy wondered. President Ayub wanted nothing of China; he’d like to see it go to hell. But the Pakistani people were anxious to do something about Kashmir. (Ref. 2)
The US amabassador to India, however, suspected that Pakistan and China were working together in 1962:
Ayub Khan's letter to the President seemed to justify all of Galbraith's fears of Pakistani collusion with China against India. (Ref. 1, P. 127)
- "The USA assured Pakistan that they will take the Pakistan's land dispute with India to the United Nations and help resolve them peacefully."
This claim is true - Yes, when Pakistani President Ayub Khan met Kennedy in the US, in 1961, he was assured that if talks on Kashmir failed, the US would indeed support Pakistan in the UN:
He wanted President Ayub to know that even if he did not succeed, he would have tried. Unless this effort succeeded, President Ayub believed that Pakistan would have to bring the case again to the U.N. Would the U.S. then support Pakistan? Yes, President Kennedy said, the U.S. would support the U.N. resolutions. President Ayub thanked him for this statement. (Ref. 2)
(Note though that this assurance was given in 1961, before China invaded India.)
In later private diplomatic talks during the 1962 Sino-India war, it appears Kennedy further committed to help with the negotiations on Kashmir if Pakistan assured India it wouldn't attack it:
Should Ayub be forthcoming, Kennedy said, “We are prepared to tell Nehru that if we give him major military aid he should agree to negotiate at a suitable point on Kashmir.” The president accompanied this carrot with a stick — a warning of the dire consequences to U.S.-Pakistan relations should the Pakistanis draw closer to China. (Ref. 3, P. 79)
- "Pakistan didn't respond to China's invitation."
This claim is partially true - As pointed out earlier, information is lax on whether China ever extended such an invitation. However, it is a fact that ultimately Pakistan didn't join China in attacking India. Multiple factors were at play behind this decision:
... A Pakistani attack in Kashmir in the fall of 1962 would have stretched India’s military to the breaking point. Three years later in 1965 Ayub Khan did attack India ... Pakistan was clearly capable of initiating war with India, but decided in 1962 not to take advantage of India’s vulnerability. One reason it did not attack was that most of India’s army and air force, and its entire navy, remained concentrated on the western border with Pakistan. The forces that were moved eastward to reinforce the endangered NEFA battlefield were infantry, and they moved slowly ... the core of the existing Indian army would remain focused on armored warfare against Pakistan.
... The Americans thus played a decisive role in forestalling a Pakistani attack on India. Kennedy’s messages to Ayub Khan, reinforced by similar messages from Prime Minister Macmillan, left little doubt that the United States and the United Kingdom would view a Pakistani move against India as a hostile and aggressive action inconsistent with the SEATO and CENTO treaties ... They asked for his assurance of neutrality. To have acted militarily would have left Pakistan isolated from its treaty allies and totally dependent on China — and Pakistan was unsure about China’s military intentions. Any Pakistani attack on India in the west would need to be based on the assumption that China would keep up the pressure in the east and in Kashmir. Ayub had no concrete reason to believe that would be the case. Like everyone else he did not know what Mao planned to do next. (Ref. 1, P. 129-130)
- "The USA didn't fulfill its promise."
This claim is false - Kennedy had committed that the US would try to resolve the Kashmir issue and, failing that, it would support Pakistan in the UN on it. All evidence indicate that Kennedy made an honest effort to mediate between India and Pakistan, and failed.
Kennedy became deeply involved in this exercise. He persuaded Eugene Black, the head of the World Bank and principal negotiator of the Indus waters treaty, to take on the assignment and personally requested Nehru and Ayub to agree to the role he proposed that Black play. Despite this presidential intercession, Nehru turned down the proposal. (Ref. 3, P. 72)
Ayub had cleverly been waiting for India to reject mediations, and used it as an excuse to pressure the US to bring this issue to the UNSC. The US tried to dissuade Pakistan but couldn't. So it helped Pakistan in the UN too. But, according to the US, Pakistan apparently misunderstood this to mean that US had committed to do all the legwork and push through any resolution proposed by Pakistan:
- Memorandum From the Assistant Secretary of State for International Organization Affairs (Cleveland) and the Assistant Secretary of State for Near Eastern and South Asian Affairs (Talbot) to Acting Secretary of State Ball
You will recall that the genesis of our intimate involvement with the Kashmir dispute before the Security Council arose during Pakistani President Ayub’s visit to the United States last year. Among other things Ayub felt that he had received a commitment from the President to support Pakistan if the issue of Kashmir were raised by Pakistan in the Security Council. After India had rejected the Black mission, Pakistan, against the advice of the United States, in fact brought the Kashmir issue to the Security Council. It soon became clear that Pakistan expected the United States to assume a major active responsibility for advancing Pakistan’s position and that an excessively broad interpretation was being placed by Pakistan on the President’s commitment. Accordingly, the Department sought to limit Pakistan’s interpretation that the United States should actively manage the Kashmir issue in the Security Council to a successful conclusion (Pakistan is not a member of the Security Council). (Ref. 4)
As the full memo (ref. 4) highlights, the US did indeed use all its diplomatic efforts to support Pakistan's resolution, that was submitted to the UN by Ireland (due to the personal request made by the US). The Irish resolution passed by a majority in the UNSC but was ultimately vetoed by the USSR, as the US had warned Pakistan it would be.
Later on, keeping its promise, the US continued pressuring Nehru to negotiate and even roped in the British too for this:
... Kennedy decided to send to South Asia a high-level mission led by veteran diplomat W. Averell Harriman ... Commonwealth Secretary Duncan Sandys headed a parallel British political-military team ... After considerable further effort by Harriman, Nehru agreed that he would enter the negotiations with an open mind and without preconditions ... Bilateral negotiations began in Rawalpindi on December 29, 1962, and dragged on through six sessions before petering out ignominiously five months later. Senior U.S. officials were deeply involved throughout the nego- tiating period, and President Kennedy himself sent personal letters to Nehru and Ayub at crucial points ... If the talks failed, it was not for lack of effort or attention on the part of the Kennedy administration. (Ref. 3, P. 80-82)
References:
JFK's Forgotten Crisis: Tibet, the CIA, and Sino-Indian War by Riedel, Bruce O
Memorandum of conversation, “Kennedy-Ayub talks,” July 11, 1961, FRUS 1961–1963, XIX
The Limits of Influence - America's role in Kashmir by Howard Schaffer
Memorandum From the Assistant Secretary of State for International Organization Affairs (Cleveland) and the Assistant Secretary of State for Near Eastern and South Asian Affairs (Talbot) to Acting Secretary of State Ball, June 22, 1962, FRUS 1961–1963, XIX