US President Donald Trump has offered to work as 'mediator, an arbitrator or a facilitator' to achieve a genuine and lasting peace between Israel and Palestine as he hosted Palestinian President Mahmoud Abbas at the White House.

In their first meeting, Trump and Abbas discussed the advancement of the Middle East peace process and the strengthening of US-Palestinian relations, the White House said in a statement.

"Trump and Abbas reaffirmed the commitment of both the US and the Palestinian Authority to achieve a genuine and lasting peace between the Israelis and Palestinians," the White House said.

Trump stressed that he is personally committed to helping the Israelis and Palestinians achieve a comprehensive peace, and that any peace settlement can only be the product of direct negotiations between the Israelis and Palestinians.

The US President expressed his appreciation for Abbas' unambiguous support for a negotiated settlement of the conflict.

Trump offered himself as a "mediator, arbiter or facilitator" to help reach a peace agreement between Israel and Palestine, but said, "Any agreement cannot be imposed by the US or any other nations."

The two leaders discussed the value of actions that can help create a climate conducive to tangible progress toward peace.

According to the White House the two leaders President reaffirmed the joint determination of the Palestinian Authority and the US to combating violence and terrorism.

They discussed the importance of the US-Palestinian partnership in building and sustaining the capacity of Palestinian security forces to counter terrorism, maintaining peace and security for the Palestinians, and continuing strong coordination with the Israeli government to benefit both peoples.

"President Trump emphasised the importance of making a clear commitment to preventing inflammatory rhetoric and to stopping incitement, and to continue strengthening efforts to combat terrorism.

"President Trump raised his concerns about payments to Palestinian prisoners in Israeli jails who have committed terrorist acts, and to their families, and emphasised the need to resolve this issue," the White House said.

"An honour to host President Mahmoud Abbas at the WH today. Hopefully something terrific could come out it between the Palestinians & Israel," Trump said in a tweet to his more than 28.6 million followers.

The White House Press Secretary Sean Spicer told reporters at his daily news conference that the two leaders discussed a wide range of issues.

"Some of the topics that were discussed during their meeting and the lunch were: advancing the Israeli-Palestinian peace; preventing incitements to violence, particularly media outlets directly associated with the Palestinian Authority; strengthening efforts to combat terrorism, including defeating Daesh; measures to empower the Palestinian economy and provide economic opportunity for the Palestinian people," he said.

"They had a series of private discussions. That is why the President is able to effectively get things done for this country is to not negotiate out in public. He's going to continue to have discussions with Prime Minister Netanyahu, President Abbas moving forward, and he feels confident about where that relationship was and developments that were made today," he said