"We have put forward to the Israelis our position on different final status issues, and especially on borders and security," Abbas told the Jordanian paper.
Israel wants to keep troops on the eastern border of any future Palestinian state, a demand that the Palestinians deem unacceptable as it would give the Israeli military a continuing presence on Palestinian soil.
Abbas has said, however, that a force from the Nato military alliance could be acceptable.
The Palestinian president also signalled that he might be willing to trade Palestinian land captured by Israel in 1967 where settlements have been built, for an equal amount of Israeli land.
"We have said that borders need to be on a 1967 basis, with agreement on land swaps equal in value and size, and we gave our vision regarding security, which was agreed on previously in Olmert's days," Abbas said, referring to Israel's former prime minister.
Negotiations between Abbas and Netanyahu's predecessor, Ehud Olmert, broke off in December 2008, during Israel's military offensive on the Gaza Strip.
Mitchell said he was "heartened" by his meeting with Abbas on Saturday, but he did not elaborate.
However, a leading figure in Abbas's Fatah party said Mitchell had not given adequate answers on the issues of borders or security.
"Mitchell did not present ... any new Israeli answers," Mohammad Dahlan said in a statement.
Before travelling to Ramallah, the US envoy held talks with Binyamin Netanyahu, the Israeli prime minister, for the latest in weeks of meeting aimed at getting the two sides to meet.
Abbas said on Saturday that the Israelis need only to recognise that his propositions are acceptable, in principle.
"If they agree, we will consider that progress ... and this would prompt us to go to direct negotiations," he said.
But Netanyahu has previously insisted that any direct talks must take place without conditions.
Mark Regev, an Israeli government spokesman, blamed the Palestinians for the deadlock. "We definitely don't want another year and a half without negotiations," he said.
Yasser Abed Rabbo, an aide to Abbas, said that a decision on direct talks is not expected before early next month.
He said the Palestine Liberation Organisation's top decision-making body and Arab foreign ministers would have to have their say on the issue, while Abbas is also waiting for clarifications from the US.