Secretary of State Hillary Clinton said Mitchell held a "good, productive" meeting in Jerusalem on Wednesday with Netanyahu, a day after he had what Crowley called a "serious and positive" meeting with Abbas in Ramallah.
Mitchell also met with Israeli Defense Minister Ehud Barak.
In the West Bank town of Ramallah, Palestinian officials on Tuesday said they had made progress towards the launch of direct talks with Israel during Mitchell's visit.
However, they adhered to the same demands that have held up talks for months, namely a complete freeze of Israeli settlement activity and set guidelines regarding the negotiation of final borders.
The Palestinians also want a set timeline for an agreement addressing all the core issues of the conflict that does not exceed 24 months.
The Palestinians reluctantly agreed to indirect negotiations in May following months of pressure from the Middle East diplomatic Quartet, made up of the United States, Russia, the European Union and the United Nations.
But they have thus far rejected demands of the Quartet to move into direct negotiations without a settlement freeze and border guarantees.
They also said the indirect "proximity" talks have made little progress.
Netanyahu has repeatedly called for direct talks, but few Palestinians believe his mostly right-wing government is prepared to withdraw from the West Bank or occupied and annexed east Jerusalem.
Crowley said details about how talks would proceed need to be worked out before the sides agree to resume direct talks that broke off in December 2008 when Israel invaded the Gaza Strip to stop Hamas militant rocket fire.
"I'm sure there will be ongoing consultations within the Palestinian Authority and the Israeli government over the next few days," Crowley told reporters.
He said that while Mitchell returned to Washington late Wednesday his deputy David Hale remained in the region for consultations.
"We are down to... some specific details that if we can resolve those, we think we'll overcome remaining hesitation," Crowley said.
Crowley said details needing to be worked out included when and where the new direct negotiations will take place and who will be involved.
"But we're also contemplating precisely... how will the negotiations unfold, what are our expectations in terms of timelines, what are milestones that we hope can be accomplished during the course of this initial phase of the negotiations," Crowley said.
"So we are working through all of these details," he added.
Crowley also said Clinton would consult further with her counterparts in the Quartet, which he expects will issue a statement in support of the peace talks.
"There's likely to be a statement of support... from the Quartet in the coming days," he added.
On Tuesday, Crowley appeared to suggest that such a statement could come as early as Wednesday, but he remained upbeat about a resumption of talks.
"We believe we are closer to direct negotiations than we were last week," Crowley said.
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