Hamas, which advocates Israel's destruction, instead recycled previous offers, including a 10-year truce if Israel takes the unlikely step of withdrawing from the West Bank and Jerusalem first.
Hamas has repeatedly confounded observers with its conflicting messages. Actions on the ground -- seven rockets were fired on Israel from Hamas-ruled Gaza on Monday, including one that wounded a 4-year-old boy -- contradicted the militant group's positive words about coexistence and a truce.
A leader of the Hamas military wing, which carried out a twin suicide bombing on the Gaza border Saturday, said his group would step up attacks against Israel in coming days.
The salvo of rockets came despite a last-minute phone call from Mr. Carter, urging a one-month halt to attacks on Israel, to gain some international goodwill and defuse tensions.
"I did the best I could," Mr. Carter said of his conversation with Hamas supreme leader Khaled Mashaal, pressing him to declare a one-month truce. "They turned me down, and I think they're wrong."
The Bush administration and Israel, which shun Hamas as a terrorist group, have criticized the Carter mission as misguided.