But after going out of his way to talk up close ties with Israel during his first year in office, Mr Trump offered a more even handed approach in the interview with the conservative newspaper Yisrael Hayom by offering a cool assessment of Israeli settlement building.
The White House also said the two leaders discussed North Korea's nuclear program, a topic not mentioned in the Kremlin's statement about the call.
The trend has always been that no matter how pro-Israel American presidential candidates sound during the election campaign, after entering the White House they always end up blaming Israel for the lack of peace.
But it sounds like Trump wants Putin to be his back channel to the Palestinians who unsurprisingly no longer consider the U.S.an "honest broker" in its relationship with Israel.
On 30 December, Trump had tweeted on street protests in various Iranian cities saying, "Many reports of peaceful protests by Iranian citizens fed up with regime's corruption & its squandering of the nation's wealth to fund terrorism overseas". However, the Israeli officials insist on maintaining the occupation of Palestinian territories.
Relations between the USA and the Palestinians have spiraled since Trump recognized Jerusalem as Israel's capital in December. Putin was the one who called Trump at that time to reportedly thank the USA leader for a Central Intelligence Agency tip that was said to have helped thwart bombings in St Petersburg. The UN voted to condemn Trump administration's decision overwhelmingly.
Abbas said last week that he hoped Russian Federation could assume a greater role in Israeli-Palestinian peace talks, saying the USA "can no longer play a leading role".
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".
"President Trump has made it clear that he is more officially and formally pro-Israel than another recent president", added Bennis, who is also a fellow at the Institute for Policy.
The Palestinians have never actually rejected peace talks, however, and have simply said in recent months, given Trump's overt hostility toward them, and declaration that Jerusalem is Israel's capital make the United States an unsuitable arbiter.