"I just spoke with American President Trump", Putin told Abbas before continuing the talks behind closed doors.
Meanhwhile, US President Donald Trump extended his condolences over the a recent deadly crash of a Russian regional passenger plane near Moscow in phone talks with Russian President Vladimir Putin on Monday, the Kremlin's press service said.
During his trip to the Middle East in May 2017, the US president told the Israeli and Palestinian leaders that they should make a compromise in order to achieve peace. He declined to give a timeline for releasing the U.S. plan for peace between the rivals.
The Arab world will have it no other way, and successive presidents (ostensibly the most powerful men on earth) have always been too afraid of upsetting the oil-rich sheikhs, emirs and military dictators. He has however noted that neither side appears to be "looking to make peace" since he officially recognized Jerusalem as Israel's capital.
The White House said Trump repeated his belief that it is time to work toward a lasting peace agreement. Nothing less. I think it is catastrophic for Israel, in how it was done, how it was allowed to be done, how it was signed, how it was agreed to, it is rather incredible to me. The Israeli settlement policies, which gathered pace following Trump's ascension to office, are widely supported by the USA ambassador to the country, David Friedman.
Israel has offered the Palestinians numerous statehood plans, but the Palestinian Authority walked away from all previous peace talks.
Wafa quoted the Russian officials as saying that Putin was looking forward to his meeting with the PA president. Late a year ago, Trump announced that the USA would recognize Jerusalem as the capital of Israel, a move that angered many Palestinians.
In the interview, Trump said that his recognition of Jerusalem as the country's capital was one of the highlights of his presidency thus far.
Abbas has refused any contact with Trump's administration since Washington's decision at the end of past year.
"Israel has to be careful with settlements", Trump warned.
Palestine views the United States' decision as a rejection of East Jerusalem as the capital of any future Palestinian state.
Monday saw an awkward turn in Prime Minister Benjamin Netanyahu's and President Donald Trump's "friends for ever" relationship, which is still being sorted out.
More than 600,000 Jews live in around 140 settlements which are considered illegal under worldwide law and were built since Israel's occupation in 1967 of the West Bank and East Jerusalem.