Mike Pence has kicked off his visit to Israel by saying it was an honour “to be in Israel’s capital, Jerusalem”.
Mr Abbas says America can no longer serve as mediator in Middle East peace talks. The Palestinians are planning a general strike on Tuesday to protest Mr Trump’s declaration.
Violent protests since Mr Trump’s announcement has left at least 17 Palestinians dead, mostly in clashes with Israeli forces. One Israeli has been killed in that time.
Mr Netanyahu said on Sunday night, referring to Mr Abbas by his Arabic nickname: “Regarding peace, I have a message to Abu Mazen.
“There’s no substitute to the American leadership in leading the diplomatic process.
“Whoever won’t discuss peace with the Americans doesn’t want peace.”
Mr Abbas is due to meet EU foreign ministers in Brussels on Monday while Mr Pence is in Israel, and is expected to ask them to officially recognise the state of Palestine “as a way to respond” to Mr Trump’s announcement.