In a speech, Carter said he heard from Hamas leaders they would "accept a Palestinian state on the 1967 borders if approved by Palestinians." He was referring to the occupied West Bank and Gaza Strip and a referendum on a deal Washington hopes to clinch this year.
"It means that Hamas will not undermine (Palestinian President Mahmoud) Abbas's efforts to negotiate an agreement and Hamas will accept an agreement if the Palestinians support it in a free vote," he said.
But Carter said Meshaal, whom he met on Friday and Saturday and telephoned on Monday over U.S. and Israeli objections, turned down his appeal for a unilateral ceasefire with Israel to end violence threatening peace efforts.
"I did the best I could on that," Carter said of his failure to persuade Hamas to halt rocket fire from the Gaza Strip.
The Nobel peace prize laureate stopped short of saying he obtained a clear commitment from Hamas to recognize Israel's right to exist, one of the conditions set by Western powers to deal with the group.