Speaking in an interview with the French radio station Europe 1, Abbas said Israel's decision to allow the construction freeze to expire had endangered the Middle East peace process.
"We demand a moratorium for the duration of negotiations, because as long as there are negotiations there is hope," he said.
Mitchell is due to hold talks with both sides this week.
His visit follows telephone discussions between US Secretary of State Hillary Clinton and Israeli Prime Minister Benjamin Netanyahu late on Monday, which a State Department spokesperson described as "very significant, very detailed, very direct".
"We believe [Netanyahu] is sincerely interested in the process, recognises its importance," said spokesperson Philip Crowley.
He added that the US appreciated the Palestinians' "restraint" in not pulling out of negotiations following the settlement freeze's expiry on 26 September.
Netanyahu's refusal to renew the moratorium has drawn international criticism, including from the US, France, Britain, the European Union and the UN.
Abbas has said that the Palestinians will give their official response to the end of the freeze next week, once he has met the Palestinian executive and Arab foreign ministers on 4 October.