Hamas released Edan Alexander, the last living American hostage it held in Gaza, on Monday evening, after mediators brokered a deal between the group and the United States that largely circumvented the Israeli government. Hamas and the Israeli military confirmed the handover.

Mr. Alexander’s release came on the eve of a visit by President Trump to the Middle East, and was portrayed by Hamas officials as an attempt to secure U.S. support for a wider deal to end the war.

Mr. Alexander, 21, was among roughly 250 people seized and taken to Gaza during the Hamas-led attack on Israel on Oct. 7, 2023, that ignited the war in Gaza. A dual Israeli American national serving in the Israeli Army, he was captured from a military post that morning. He grew up in New Jersey and moved to Israel after high school to join the military.

Unlike most other hostages, Mr. Alexander was released without a formally announced cease-fire between Israel and Hamas, highlighting the failure of efforts to secure a broader truce between the two sides. Hamas still holds at least 20 living hostages — along with some 40 dead bodies, including those of several Americans — but it is reluctant to release more of them unless Israel agrees to hold negotiations to end the war. Israel wants the right to continue the war after any future truce, leading to an impasse in the talks.

Benjamin Netanyahu, the Israeli prime minister, said in a statement on Monday that Mr. Alexander’s release showed the benefits of placing Hamas under greater military pressure. In March, Mr. Netanyahu ordered the Israeli military to break an earlier cease-fire, saying it would force the group to release more hostages and lead to its total military defeat.

But critics of Mr. Netanyahu’s strategy have said Mr. Alexander’s release instead highlighted the failure of such an approach, since he was being released mainly because of U.S. pressure rather than Israeli action. Growing numbers of Israelis support securing a deal to free all hostages, even if such a truce would require Mr. Netanyahu to compromise, end the war, and allow Hamas to survive. Mr. Netanyahu announced on Monday that he would send a delegation to join negotiations for a temporary cease-fire, disappointing those who want him to agree to a permanent truce in order to free all the hostages.