"The Russian leader noted the depth and quality of the Russian-Palestinian relations and suggested the talks be focused on the situation in the region and bilateral ties", TASS reported, noting that Putin commented that the situation in the region "is far from what we want to see".
Abbas has refused any contact with Trump's administration since Washington's decision at the end of a year ago.
In an interview with Reuters last month, Trump accused Russian Federation of helping North Korea evade sanctions imposed by the United Nations Security Council, saying that "Russia is not helping us at all with North Korea".
Putin met Israeli leader Benjamin Netanyahu exactly two weeks ago in Moscow.
President Trump also offered his condolences to President Putin on Monday for the crash outside that killed 71 people, the Kremlin and White House both said.
Authorities confirmed on Sunday that all 65 passengers and six crew members aboard a Saratov Airlines flight died earlier that day after the plane crashed just outside the Russian capital. He said last week that he hoped Russian Federation could assume a greater role in Israeli-Palestinian peace talks, saying the United States "can no longer play a leading role".
The White House denied Netanyahu's claims, in a rare public show of disunity. The statement by Prime Minister Benjamin Netanyahu that talks with the United States has been on over the possibility of Israel annexing Jewish settlements in the occupied West Bank, drew swift condemnation from Palestinian leaders.
On Nov. 29, 2012, Palestine was designated a non-member observer United Nations state after a General Assembly vote, allowing Palestinians to join global organizations, including the worldwide Criminal Court.
Palestine claims Israeli-occupied East Jerusalem as the capital of a future independent state, although Israeli settlements - in defiance of United Nations resolutions - are gradually annexing the city and its outskirts.