Sharon was not due to hold talks with US government officials during the trip which is described as a private visit.
He arrived in the United States ahead of Palestinian President Mahmoud Abbas, who is to meet US President George Bush at the White House on Thursday.
Abbas and Bush are expected to discuss Middle East peace moves after Israel evacuates all 21 illegal Jewish settlements in Gaza and four of 120 in the West Bank in August.
On the flight to New York, Sharon said there would be no delay in starting the so-called disengagement.
A senior security source said on Sunday that some top officers wanted to delay the withdrawal due to slow preparations and worries over the strength of Palestinian resistance groups.
"This report has no basis. The disengagement is to be carried out on the exact date that has been set," Sharon said.
"I think it will begin on the 16th or the 17th [of August]."
Sharon is to attend a rally in his honour in New York later in the day, hosted by US Jewish organisations.
He was to deliver a policy speech in Washington on Tuesday to the Israel-American Public Affairs Committee, the most powerful pro-Israel lobbying group in the United States.