Abbas has said the United States can no longer be a mediator in talks, following US President Donald Trump's controversial December 6 recognition of Jerusalem as Israel's capital.
Saleh Raafat, a member of the Palestinian delegation visiting Russia, said Abbas had tasked the delegates with pushing Chinese and Russian leaders to back peace talks.
"We are now in Russia, and some of us will go to Beijing to deliver the same message on the importance of seeking international sponsorship for the peace process under the banner of the United Nations," Raafat told AFP by phone from Moscow.
On Monday, Abbas reiterated his opposition to any US role as broker between the two sides, saying "whoever allows the United States to return as a partner or mediator in the peace process is crazy".
Peace talks between Israel and the Palestinians have been frozen since they collapsed in 2014.
Trump had said he was keen to restart them to push for the "ultimate deal", but his Jerusalem recognition infuriated the Palestinian leadership.