Such a referendum, he said, would have to be voted on by Palestinians living all over the world. They number about 9.3 million, including some 4 million living in the West Bank, Gaza and east Jerusalem.
The only senior Israeli official to meet with Carter during the former president's latest Mideast mission was Israeli President Shimon Peres. During their meeting, Peres scolded Carter for meeting with the Islamic militant group.
Israel says Carter's talks embolden Palestinian extremists and hurt Palestinian moderates as they try to make peace with the Jewish state. Abbas, who rules only the West Bank, is in a bitter rivalry with Hamas.
"The problem is not that I met with Hamas in Syria," Carter said Monday. "The problem is that Israel and the United States refuse to meet with someone who must be involved."
Carter said Israeli-Palestinian peacemaking has "regressed" since a US-hosted Mideast conference in Annapolis, Md., in November. He faulted Israel for continuing to build on disputed land the Palestinians want for a future state and for its network of roadblocks that severely hamper Palestinians traveling in the West Bank.
"The prison around Gaza has been tightened," he said, referring to Israel's blockade of the territory since the Hamas takeover.
Israel has been negotiating directly with Abbas, who heads a moderate government based in the West Bank. Abbas lost control of the Gaza Strip last June.
Carter said Hamas has promised to let a captured Israeli soldier send a letter to his parents.
Direct communication between Israel and Hamas could facilitate the release of Cpl. Gilad Schalit, who has been held in Gaza for nearly two years.
Israel agrees in principle to release 1,000 Palestinian prisoners in exchange for Schalit, but after back-and-forth talks through Egyptian intermediaries, has approved only 71 of the specific prisoners that Hamas wants freed, he said.