The split screen seemed to capture Israel's mood of frustration over its setbacks in recent years.

On one side, television viewers saw the somber face of Ehud Olmert as he addressed them Tuesday evening for perhaps the last time as prime minister. His message: Marathon efforts to win the release of a captured soldier had failed.

The other side showed the soldier's dejected parents as they listened from a tent outside Olmert's residence.

The tent had been pitched by advocates of a prisoner exchange with the soldier's Palestinian captors, amid high expectations of a deal before Olmert leaves office in the coming days.

But the Israeli leader announced that government negotiators had gone as far as they could, offering to release most, but not all, of the imprisoned militants on the captors' list.

"These proposals were rejected," he said. "No others will be offered."

Olmert's three years in office have been marked by a series of disappointments: inconclusive battles against Islamic militants in Lebanon and the Gaza Strip; fruitless peace talks with the Palestinian Authority; a mounting sense of insecurity in the face of regional threats; corruption scandals that forced the prime minister to end his term a year ahead of schedule.

But to many Israelis, his failure to bring home Staff Sgt. Gilad Shalit is the most poignant of all.

Shalit's ordeal has gripped a nation where 18-year-olds are drafted into the army and the military prides itself on never abandoning its own.

The tank crew member, now 22, was seized by militants in June 2006 and spirited across the border into the Gaza Strip. Two fierce assaults in Gaza failed to free him from an incommunicado detention by the territory's Hamas rulers that is now in its 997th day.

Israelis have waged an intense debate in recent weeks over the morality of releasing Palestinian prisoners responsible for suicide bombings of buses, cafes and nightclubs during an uprising early in this decade.

But the high-profile campaign for Shalit's release, joined by several Cabinet ministers, created expectations that Olmert would meet Hamas' demands and bring closure to a case that has dogged him since the month after his election.

The latest round of indirect negotiations with Hamas ended Monday in discord.

Working through Egyptian mediators in Cairo, Hamas had demanded the release of 450 prisoners convicted of having masterminded or otherwise been involved in bombings and other deadly assaults.

Israel offered to free 320 from that list, officials said, but insisted on deporting some of them beyond Israel and the Palestinian territories. Olmert's office released the names of 10 of the prisoners Israel refused to free because of their involvement in the worst attacks.

"We have red lines," Olmert said in his televised address. "We won't cross them."

Hamas rejected the offer. Osama Hamdan, the Hamas representative in Beirut, said Israeli negotiators had pressed for its acceptance by warning that Prime Minister-designate Benjamin Netanyahu would be less disposed to a prisoner exchange.

But Israel's offer fell short of "the bare minimum" acceptable to Hamas, Hamdan said in a statement on the militant group's website.

"As soon as there is a serious offer from Israel," he said, "we will deal with it."

The impasse over Shalit has a bearing on tensions in the region. Olmert had made his release a condition for a formal cease-fire with Hamas and a lifting of a blockade of Gaza. The Obama administration and other Western governments have been pressing Israel to take such steps in order to speed repairs of Gaza's devastation in a recent Israeli military assault aimed at stopping Hamas' rocket attacks.

Olmert insisted that his government had "spared no effort" to win the soldier's release. "Unfortunately," he said, "we came upon a cruel organization, murderous and merciless, that wasn't ready to answer the challenge."

Noam Shalit, the young man's father, was visibly disappointed.

Surrounded by supporters in the tent, he offered a televised rebuttal: "Instead of offering explanations as to why his efforts failed, he should begin to truly and vigorously work and bring real results during the days he still has left to bring Gilad back."

But even before Olmert spoke, Israeli commentators were saying that time had run out.

"The gap between the two parties' positions is too large, and the time that Olmert has left in office is too short," columnist Nahum Barnea wrote in Tuesday's edition of Yediot Aharonot. "Of all the obligations that Olmert will be leaving behind for the Netanyahu government, releasing Shalit is the one that involves the greatest degree of heartache."