"I just spoke with American President Trump," Putin told Abbas before continuing the talks behind closed doors. "Obviously we spoke about the Israeli-Palestinian conflict."
The Palestinian leader was visiting Moscow in a bid to secure Putin's support after Trump outraged the Palestinians and their allies by recognising Jerusalem as Israel's capital.
The "situation is far from what we want to see," Putin said, adding that he has "always supported the Palestinian people".
"It is very important for us to know your personal opinion in order to set the record straight and put in place a common approach to solve this problem," Putin told his guest.
Trump told Putin that "now is the time to work toward an enduring peace agreement", according to a White House statement.
Abbas has refused any contact with Trump's administration since Washington's decision at the end of last year.
"Given the atmosphere created by the United State's actions, we ... refuse any cooperation with the United States as a mediator," said Abbas.
"In case of an international meeting, we ask that the United States be not the only mediator, but just one of the mediators."
Netanyahu on Monday said he had been in talks with Washington about annexing settlements in the occupied West Bank, a move condemned by a top Palestinian official as "land theft".
The White House denied Netanyahu's claims, in a rare public show of disunity.
Palestinians see the US Jerusalem decision, which broke with years of international diplomacy, as a denial of their claim to East Jerusalem as the capital of an eventual Palestinian state.
Abbas, who is due to speak at the United Nations Security Council on February 20, has promised his people to work towards full recognition of a Palestinian state by the UN.
Palestinian statehood is recognised by more than 130 countries.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)