But the American government had vetted all of the Fulbright winners for security as well as for academic achievement. Ms. Rice said that unless there was something significant she did not know about the three men that the Israelis could present to her, she wanted them to be permitted to leave.

The three  Zuhair Abu Shaaban, 24, Osama Dawoud, 25, and Fidaa Abed, 23  studied at the Islamic University of Gaza, a Hamas stronghold, which is perhaps the reason Israel has concerns about them. But all said in interviews on Sunday that they had studied there because it was the only institution in Gaza that offered the engineering fields they wanted to pursue and that they had never been involved in Hamas or politics of any kind.

“I don’t support Hamas,” Mr. Dawoud said. He is hoping to be able to accept the offer to study for a doctorate in environmental engineering at the University of Utah.

Mr. Abu Shaaban, who has been accepted into a master’s program in electrical engineering at the University of Connecticut, said that he had been permitted to cross into Israel, where security officials interrogated him for two hours. They told him they would let him leave if he gave them information on several dozen members of his extended family who they believed were associated with Hamas. Mr. Abu Shaaban said he had told them that there were more than 10,000 Gazans with his last name and of those on the list given to him, he recognized only 4. They then sent him home, he said.

“I am not guilty,” he said Sunday. “Please tell everyone I have nothing to do with Hamas. All I want in life is to get an education and come back to serve my community.”

Mr. Abed, who was accepted into a master’s program in computer engineering at Columbia University, is also hoping that the Israelis change their minds.

Major Lerner said Israel was examining the cases of students who had been offered grants from Europe. In a change of policy announced a week ago, Israel will no longer systematically bar Gazans from leaving to accept fellowships to study abroad. But those with grants must pass through an Israeli security check and, he said, the three Fulbright grantees had failed it.