Downing Street said it was "confident we can move forward" after Mr Mitchell briefed Tony Blair at Number 10 on the chances of breaking the impasse over the refusal of the IRA to begin decommissioning its weapons.
Mr Mitchell, who is due to publish his conclusions next week, said he had asked the parties to assess the chances of decommissioning beginning.
"I have made no secret of the fact that I would like to complete this as soon as possible," he said in Downing Street. "I will not impose any specific date as a deadline, I am going to do the best I can."
Mr Mitchell briefed the Irish premier, Bertie Ahern, in Dublin on Tuesday before leaving for Washington. He will consult the international decommissioning body before returning to Stormont on Monday for further talks.
During a visit to Hungary, Mr Ahern said: "For the third time this year, I think we're at a very difficult stage in the negotiations to get full implementation of the Good Friday Agreement." But, he added: "It's still at the stage of hope rather than certainty."
Downing Street denied that the talks were near to breaking down, despite the departure for a tour of America by David Trimble, the leader of the Ulster Unionists and First Minister in the Northern Ireland Assembly.
Mr Mitchell is believed to be seeking the confidence of the opposing sides to "jump together," encouraging the Unionists to form a power-sharing executive with Sinn Fein and persuading the Sinn Fein leadership to guarantee that decommissioning will start.
Two nephews of Gerry Adams, the Sinn Fein president, Liam McCorry, 18, and his brother Micheal, 15, were killed in a car crash in Belfast last night.Reuse content