Mostly Yes, the National Security Entry-Exit Registration System (NSEERS).
It was introduced in 2002 by Attorney General John Ashcroft. You can view his prepared remarks here:
The second component of the system is periodic registration. This will only apply to those individuals of elevated national security concern who stay in the country for more than thirty days. They will have to register at an INS office and simply verify that they are doing what they said they came to America to do and living where they said they would live. Such registration will be required at the 30-day point, and every 12 months after the date of entry. Aliens already in the United States who fall into categories of elevated national security concern will be asked to come in and register as well.
ICE still has a PDF available here describing the special registration procedures, and other things that would be expected of non-immigrant visitors. From that PDF:
The above will apply only to persons who want to enter the United States for a temporary period of time
(such as a tourist or a student, etc.). Persons who have been approved to stay permanently in the United
States do not have to follow special registration procedures at this time.
I was able to locate the underlying regulations by finding the DHS rule that removed them. 8 CFR 264.1(f) includes the following:
(f) Registration, fingerprinting, and photographing of certain nonimmigrants. (Paragraph (f) revised 12/2/03; 68 FR 67578) (Paragraph (f) revised effective 9/11/02; 67 FR 52584)
(1) Registration requirement for certain nonimmigrants. Notwithstanding the provisions in paragraph (e) of this section, nonimmigrant aliens identified in paragraph (f)(2) of this section are subject to special registration, fingerprinting, and photographing requirements upon arrival in the United States. This requirement shall not apply to those nonimmigrant aliens applying for admission to the United States under sections 101(a)(15)(A) (8 U.S.C. 1101(a)(15)(A)) or 101(a)(15)(G) (8 U.S.C. 1101(a)(15)(G)) of the Act. In addition, this requirement shall not apply to those classes of nonimmigrant aliens to whom the Secretary of Homeland Security and the Secretary of State jointly determine it shall not apply, or to any individual nonimmigrant alien to whom the Secretary of Homeland Security or the Secretary of State determines it shall not apply. Completion of special registration pursuant to this paragraph (f) is a condition of admission under section 214 of the Act (8 U.S.C. 1184) if the inspecting officer determines that the alien is subject to registration under this paragraph (f) (hereinafter "nonimmigrant alien subject to special registration").
(2) Identification of aliens subject to registration at ports-of-entry. Nonimmigrant aliens in the following categories are subject to the requirements of paragraph (f)(3) of this section:
(i) Nonimmigrant aliens who are nationals or citizens of a country or territory designated by the Secretary of Homeland Security, in consultation with the Secretary of State, by a notice in the Federal Register;
(ii) Nonimmigrant aliens whom a consular officer or an inspecting officer has reason to believe are nationals or citizens of a country or territory designated by the Secretary of Homeland Security, in consultation with the Secretary of State, by a notice in the Federal Register; or
(iii) Nonimmigrant aliens who meet pre-existing criteria, or whom a consular officer or the inspecting officer has reason to believe meet pre-existing criteria, determined by the Secretary of Homeland Security or the Secretary of State to indicate that such aliens' presence in the United States warrants monitoring in the national security interests, as defined in section 219 of the Act (8 U.S.C. 1189), or law enforcement interests of the United States.
The change was that the Attorney General (as provided for in 8 U.S.C. §1305 ), DHS, or the State Department could modify who was subject by publishing a notice in the Federal Register. The INS and DOJ published such a notice:
(a) Scope. Except as provided in paragraph (g), an alien is required to register pursuant to this Notice if the alien:
(1) Is a male who was born on or before November 15, 1986;
(2) Is a national or citizen of one of the countries listed in paragraph (b) who was inspected by the Immigration and Naturalization Service and was last admitted to the United States as a nonimmigrant on or before the relevant date specified in paragraph (b); and
(3) Will remain in the United States at least until December 16, 2002.
(b) Designated countries. This Notice is applicable to nationals or citizens of Iran, Iraq, Libya, Sudan, or Syria who were inspected and last admitted to the United States on or before September 10, 2002. This Notice is applicable to any alien who is a national or citizen of a designated country, notwithstanding any dual nationality or citizenship.
It should not be construed to mean that removing these regulations removes these same requirements from individuals visiting the United States from any country. From the DHS rule removing them:
The regulatory structure pertaining to NSEERS no longer provides a discernable public benefit as the program has been rendered obsolete. Accordingly, DHS is removing the special registration program regulations.
The information that was previously captured through NSEERS is now generally captured from nonimmigrants through other, more comprehensive and efficient systems.
From Wikipedia, the country of origins required to register were named on four different occaisions, giving the following list:
Group 1: Iran, Iraq, Libya, Sudan or Syria
Group 2: Afghanistan, Algeria, Bahrain, Eritrea, Lebanon, Morocco, North Korea, Oman, Qatar, Somalia, Tunisia, the United Arab Emirates, Yemen
Group 3: Pakistan, Saudi Arabia
Group 4: Bangladesh, Egypt, Indonesia, Jordan, Kuwait
The deadlines for registration were December 16, 2002 (Group 1), January 10, 2003 (Group 2), February 21, 2003 (Group 3), March 28, 2003 (Group 4). The deadlines for Group 1 and 2 registration were later extended until February 7, 2003. The deadlines for Groups 3 and 4 were extended to March 21, 2003 and April 25, 2003.
The program under the Bush Administration did target foreign nationals wishing to visit for a non-permanent stay, and it applied to those whose country of origin is from "a number of predominantly Muslim countries." Without too much research into all of those countries, North Korea is the only one that sticks out as the only non-"predominantly Muslim" country in the list.
I think that the only thing left unanswered is if in practice the program targetted men and only men. I didn't find any specific notices expanding the applicability of the program or any reports indicating that it had been applied to a specific individual female, however I imagine it could have been applied to women as well if someone at some level of government wanted it to, either in the general case or in the case for any specific individual visitor.