Partial answer: I don't know, and neither do the Wikipedia editors
Some additional context is given by Dankula on the Wikipedia talk page (Google Translated with minor copyedits and added notes):
Apparently, there was a typo. Mr. Begin did not tell Oriana Fallaci "I am a former terrorist" either in jest or metaphor. Instead, he started a non-humorous speech in America in front of hundreds of people (including Reagan) with this sentence. "I am a former terrorist". Unfortunately, I do not have access to the original speech (currently) and I trusted Ms. Fallaci and quoted her interview with [former Israel PM Ariel] Sharon. In this interview, both people (Ms. Fallaci and Mr. Sharon) agree that this sentence was said, and even Mr. Sharon, like my good friend [fellow Wikipedia commenter] Sinbad, did not try to make it look like a metaphor or a joke. Rather, it justifies that the target of the King David Hotel bomb  and other Haganah, Irgun, and Stern terrorist bombings were British soldiers, and it remains silent on Fallaci's question about the civilians killed. Therefore, even Mr. Sharon does not question the principle of the case and does not interpret it as a joke or a metaphor. The original speech was delivered in the presence of President Reagan [elected 1980] and during Begin's imposed trip to America shortly before the bombing and attack on Beirut [in 1983?], which probably Sinbad Garami can achieve better than us. I really recommend reading Mr. Sharon's 1982 interview
Sharon's 1982 interview is quoted in part on The Free Library and FPIF. The exact citation is "The Washington Post, August 29, 1982, front page, pp. 18, 19)". Unfortunately, here I hit a wall as I cannot access (or even find) that article. This probably couldn't have included all the information either, since it was a 10-hour interview, so maybe it's published elsewhere too (and in a language that's more decipherable than Persian).
As for the speech itself, Begin visited the US about a dozen times while PM (and before the interview). Begin and Reagan met on several occasions, such as September 9, 1981, a day later and June 21, 1982, but I don't think these were in New York nor is there anything else that even looks close to the line in question. Begin did give at least one speech in NY in 1978 (May 4th?), though I can't find the full text of that and it's not clear if not-yet-President Reagan was there. He did meet with Carter later in 1978 in NYC, but again I have no real details. Thus the second wall that I've hit.