Abbas sent a "letter of designation" to Rami Hamdallah, who is currently serving as premier within the West Bank-based government, an official in Ramallah said.
"The government is ready, but there is only one problem, and that is that Fatah and Hamas reject Riyad al-Malki as foreign minister, something Abbas is insisting on," the official told AFP, speaking on condition of anonymity.
Malki is a veteran diplomat who has served as foreign minister since 2007.
The Palestinian official later said Hamdallah had received an invitation to travel to Washington.
"The US administration today sent an invitation to the prime minister to go to Washington and meet White House and Congress officials," he said.
"This is recognition of the consensus government by the US administration."
Hamas and the Western-backed Palestine Liberation Organisation, which is dominated by Abbas's secular Fatah party, signed a surprise reconciliation agreement on April 23 to end years of bitter and sometime bloody rivalry.
The agreement gave them five weeks to set up a unity government which was to have been announced by May 28.
"If this issue is resolved today and Abbas agrees not to appoint Malki, then the government will be announced in the next few hours," the official said.
