GAZA — President Carter said yesterday that Hamas had promised it would accept a Palestinian Arab state in only part of the territory traditionally claimed, implicitly accepting Israel’s right to the remainder.

But leaders of the powerful Islamist terrorist group insisted that they would never explicitly accept the right of Israel to exist.

While Mr. Carter sought to present the development as a major breakthrough, the American administration was less impressed.

“I can’t see that anything’s fundamentally changed here,” a State Department spokesman, Tom Casey, said.

A White House spokesman, Dana Perino, said Hamas had broken promises in the past and should be judged on whether it stopped firing rockets from Gaza at Israeli towns.

While Hamas has hinted before at limiting a future Palestinian Arab state to Gaza and the West Bank, Mr. Carter sought to present their assurance as significant. He was speaking after a nine-day tour of the Middle East during which he broke diplomatic ground by meeting the Hamas leadership exiled in Damascus.

America, the European Union, Russia, and the United Nations all refuse to speak officially to Hamas on the grounds that it is a terrorist organization, although Mr. Carter said this diplomatic boycott must end for a political solution to be reached in the Israeli-Palestinian Arab conflict.

Mr. Carter said the leader of Hamas based in Syria, Khaled Meshaal, said it would accept any outcome of current peace talks between Israel and the non-Hamas Palestinian leadership as long as it was agreed by a popular referendum.

Speaking later in Damascus, Mr. Meshaal said, “We agree to a [Palestinian] state on pre-’67 borders, with Jerusalem as its capital, with genuine sovereignty, without settlements but without recognizing Israel.”