Jerusalem (CNN) -- Special U.S. Envoy George Mitchell is expected to meet with Israeli Prime Minister Benjamin Netanyahu Wednesday -- a day after he huddled with Palestinian President Mahmoud Abbas in the West Bank.
State Department spokesman P.J. Crowley said Mitchell held a "serious and positive" meeting with Abbas Tuesday.
The meetings are part of the latest push by the United States to get the parties to resume direct peace talks.
The United States also is pushing diplomacy by the Mideast Quartet to help advance the process.
"We are consulting with the Quartet and looking to see how we can encourage the parties to begin direct negotiations," Crowley said.
The parties are taking part in "proximity talks," in which Mitchell has been shuttling between the sides with little substantial progress.
Netanyahu has repeatedly called for direct talks, but Abbas has resisted months of intense pressure from the United States, the Quartet and Arab leaders to return to the negotiating table without a complete halt to Israeli settlement activity and a clear framework, agenda and timeline for the talks once they begin.
Palestinian sources expect Abbas to announce his willingness for direct talks shortly.
Crowley suggested a statement urging talks from the Quartet -- which includes the United States, Russia, the European Union and the United Nations -- could come as early as Wednesday.
He said U.S. Secretary of State Hillary Clinton has spoken in recent days with U.N. Secretary-General Ban Ki-moon, Russian Foreign Minister Sergey Lavrov and former British Prime Minister Tony Blair, the special Quartet representative.
"If a Quartet statement can be helpful in encouraging the parties to move forward, obviously, I think that's something that we, the United States, support," Crowley said.
Senior State Department officials said they expected the Quartet to invite the parties for talks.
President Barack Obama has urged the parties to begin talks before September, when an Israeli moratorium on settlement activity expires. Quartet and Israeli diplomats and aides to Abbas said the talks could begin after the Muslim month of Ramadan, which ends on September 10, or possibly on the sidelines of the U.N. General Assembly in late September.
CNN Senior State Department Producer Elise Labott contributed to this report