Vance and Israel's Prime Minister Benjamin Netanyahu, who according to The Times of Israel is to meet in Jerusalem on Wednesday, are reported to discuss upcoming phases of the peace plan for Gaza.
On Monday, the Israeli leader was however extremely vague.
We will talk about two things, above all the security challenges and the diplomatic opportunities we face, he said in the Knesset.
On Monday, a meeting was held between Netanyahu and Trump's son-in-law and adviser Jared Kushner and the US special envoy Steve Witkoff, who is also on site in Israel. The meeting was "very good", says an employee at Netanyahu's office to The Times of Israel on Tuesday.
It was about things they agreed on from the beginning, he says.
There was no disagreement there. Everything was really clear between the two parties.
On Tuesday, Witkoff and Kushner have, among other things, met Israeli hostages who were released by Hamas as part of the peace agreement in the Gaza war.
The visits come at the same time as The New York Times reports that the US fears that Netanyahu may torpedo the ceasefire.