Republican presidential nominee-in-waiting John McCain called on Obama to repudiate Carter in a speech Monday.
Obama told the Jewish group he had a fundamental disagreement with Carter, who was rebuffed by Israeli leaders during a peace mission to the Middle East this week.
"We must not negotiate with a terrorist group intent on Israel's destruction," Obama said.
"We should only sit down with Hamas if they renounce terrorism, recognize Israel's right to exist, and abide by past agreements," he added.
Obama has been working to reassure Jewish voters nervous about his candidacy in the wake of publicity about anti-Israel sentiments expressed by his pastor, the Reverend Jeremiah Wright.
Obama's rival, Hillary Rodham Clinton, also criticized him during a February debate, saying he did not immediately rejected an endorsement from black Muslim leader Louis Farrakhan. Obama responded that he already denounced Farrakhan, but would reject his support as well.
Obama told the group that he had not been aware of Wright's more incendiary speeches before launching his presidential campaign last year, even though he had been a member of Wright's congregation for nearly 20 years. Obama said he had spoken to Wright and privately conveyed his concerns about some of his sermons once he learned of their content. But he acknowledged that he had declined to be more public in his criticism until recently, since Wright was preparing to retire from ministry at Chicago's Trinity United Church of Christ.
"You make a decision about how are you going to handle it," Obama said. "Do you publicly denounce his comments? Do you privately express concern but recognize you are still part of a broader church community that is going to be transitioning? I chose the latter."
Obama has stepped up his outreach to the Jewish community in recent weeks after videos of Wright's speeches surfaced where he criticized Israel and expressed sympathy for the Palestinian cause.
Among other things, Wright has denounced Israel as racist and suggested tension between Israel and the Palestinians had contributed to the Sept. 11, 2001, terrorist attacks.
Obama also met privately with about 100 Jewish leaders in Ohio before that state's primary March 4.
Obama has been the subject of persistent Internet rumors suggesting he is a Muslim who was educated at a Madrassah in Indonesia and took the oath of office with his hand on a Koran. Obama did spend part of his childhood in Indonesia but attended Catholic and public schools there. He took the oath of office on a Bible.
Obama delivered a well-received speech last month addressing the Wright controversy, in which he criticized many of his former pastor's views. But the issue has continued to dog him.
Obama told Jewish leader he would work as president to diminish tensions between the black and Jewish communities, noting that both groups shared the experience of suffering discrimination.
Obama also said at the meeting that he is willing to make diplomatic overtures to Iran even though it has funded Hamas and other militant groups.