Trump envoy meets Palestinian leader Mahmoud Abbas

US President Donald Trump's Middle East envoy held his first talks on Tuesday with Palestinian President Mahmoud Abbas. 

The meeting took place amid continued Palestinian concern that the new US government is leaning heavily towards Israel.

Jason Greenblatt met with Abbas in Ramallah, the seat of the Palestinian Authoirity, a day after holding talks with Israeli Prime Minister Binyamin Netanyahu in Jerusalem.

"President Abbas & I discussed how to make progress toward peace, building capacity of Palestinian security forces & stopping incitement," he tweeted after the meeting.

According to a statement from the US Consulate General, the pair "reaffirmed the commitment of both the Palestinian Authority and the United States to advance a genuine and lasting peace between Israel and the Palestinians".

The statement added that President Abbas emphasised the two-state solution as the Palestinians' strategic choice.

Abbas reportedly told Greenblatt he believed "a historic peace deal was possible" under Trump's leadership. This optimism was expressed by the Palestinian leader despite Trump's own ambivalence over the two-state solution - a mainstay of US Middle East policy for two decades.

"I'm looking at two-state and one-state, and I like the one that both parties like ... I can live with either one," the US president reporters in February, sending diplomatic shockwaves across the world.

Peace talks between Israel and the Palestinians have stalled since 2014, when negotiations broke down due to deep-set disagreements over several key issues, including the continued construction of Israeli settlements on Palestinian land.

The issue was discussed by Greenblatt and Netanyahu on Monday, "with the hope of reaching a formula that will aim to promote peace and security", the Israeli PM's office said.