JERUSALEM, June 26 – The Palestinian Authority president, Mahmoud Abbas, ordered his security services on Monday to find a kidnapped Israeli soldier in the Gaza Strip. The Israeli prime minister, Ehud Olmert, warned of “comprehensive and ongoing military action” in Gaza by the Israeli military, which massed troops and armor on the border.

Tensions were building over the fate of the soldier, Cpl. Gilad Shalit, 19, who was captured early Sunday morning in a raid by Palestinians into Israel through a long tunnel from Gaza. The groups holding him said that before any information on him would be disclosed, Israel must release all Palestinian women in its jails and all Palestinian prisoners under the age of 18.

Israel rejected the demand from the groups, which include the Popular Resistance Committees; the Army of Islam, a new grouping; and the military wing of Hamas, the group that is running the Palestinian government.

There are 95 Palestinian women and 313 Palestinians under 18 in Israeli jails, of a prison population of about 9,000 Palestinians.

The Israeli call for the release of Corporal Shalit, who also holds French citizenship, was echoed by many nations. Egyptian and French diplomats took a leading role in Gaza in trying to persuade the armed groups to let the corporal go.

As those efforts continued, Mr. Olmert spoke in Jerusalem. “Yesterday, I ordered the heads of the army to deploy our forces in order to be ready for comprehensive and ongoing military action, in order to strike at the terror organizations, their commanders and anyone involved in terror,” he said. “Let it be clear. We will find them all, wherever they are, and they know it. Let it be clear that no one will be immune.”

He said later: “We will react against each and every terrorist and against each and every terror organization wherever it may be. They know we can reach them even when they believe they are safe. We do not act under pressure and therefore we have weighed our steps with patience. But the time leading towards an extensive, stern and harsh operation is growing shorter.”

Mr. Olmert made it clear on Sunday that Israel holds the Palestinian Authority – from its president, Mr. Abbas, of the opposition Fatah party, to the Hamas prime minister, Ismail Haniya – responsible for the attack and the fate of Corporal Shalit.

There is a wide expectation among Israeli officials and analysts that Israel will strike back in Gaza, but how hard, and with what means, is likely to depend on the corporal’s fate.

Israeli officials said Monday that the seizure of a soldier seemed to be a prime aim of the Palestinian raid, in which two Israeli soldiers were killed, along with two of the attackers. They said the militant groups, led by Hamas, were following the model of the Hezbollah militia in southern Lebanon and would try to bargain to release prisoners.

Corporal Shalit is being held by senior members of Hamas’s military wing, according to a senior military intelligence officer who spoke to the Foreign Affairs and Defense Committee of the Israeli Parliament. The soldier’s whereabouts are not known but he is believed to be “alive and lightly wounded,” one of the legislators quoted the officer as saying.

Still, other officials were puzzled that the groups did not release a video or some other proof that the soldier is alive.

The intelligence official also said that Mr. Haniya, the Hamas prime minister, was at odds with the military wing of Hamas, believed by Palestinians and Israelis to be under the command of the exiled Hamas leader, Khaled Meshal, who lives in Damascus, Syria.

Ghazi Hamad, the spokesman for the Hamas government in Gaza, said in an interview that Mr. Haniya and the government were not a party to the raid. “We are not involved in military action,” he said. “We are never involved with this. All the Palestinian factions have military wings and political wings. This is because we are still in a liberation stage and a building stage.”

But in an interview with The New York Times 10 days ago, Mr. Hamad insisted that Hamas was one organization with a single leadership, making decisions collectively.

On Monday, Mr. Hamad, reflecting the more anxious and responsible tone of the government, said Mr. Haniya was urging the militants “not to harm” the corporal “and to respect him as a prisoner.” But Mr. Hamad stopped short of urging the groups to release him.

On Monday, after a briefing by the Israeli foreign minister, Tzipi Livni, the American ambassador to Israel, Richard H. Jones, said, “This is a demonstration of the inability of the Hamas government so far to control its own ranks, let alone provide for the needs of the Palestinian people, and I think the world should think very hard about how we deal with an entity that can’t even control its own house.”

Efraim Halevy, the former head of the Israeli spy agency, Mossad, a senior adviser to three prime ministers and former head of the National Security Council, said the Shalit affair posed a serious test to Hamas, whether it could get its own house in order “and act like a responsible government.” If so, he said, “it could be a turning point” in the way the world views Hamas.

But Hamas officials in power in Gaza, like Mr. Haniya, must show they are in charge of Palestinian affairs, Mr. Halevy said. “If Hamas doesn’t control its own forces, it’s a problem not only for them but for Israel and all others who deal with them,” he said.

The raid and kidnapping were also a deep embarrassment to Mr. Abbas. “If it ends badly, if Abbas is shown to be less and less relevant than before, then he will be the big loser,” Mr. Halevy said.

He suggested that Israel felt a deep sense of political urgency. “Israel is prepared to take very serious military action,” he said. “The warnings must be taken very seriously. This is not an event to which Israel can turn a blind eye.”

Israeli officials have been confronted with a series of high-profile kidnappings in recent years.

In October 1994, Cpl. Nachshon Wachsman, who held joint American and Israeli citizenship, was kidnapped and held by Hamas gunmen. Hamas demands for the release of its leader, Sheik Ahmed Yassin, and 200 Hamas prisoners were rejected by Yitzhak Rabin, then prime minister. He ordered a rescue attempt, but Corporal Wachsman and the Israeli unit commander were killed.

Israel has at times also made deals and exchanged prisoners. In October 2000, Hezbollah abducted three Israeli soldiers in an effort to free imprisoned leaders. The soldiers were apparently murdered or died during the abduction or soon afterward. The same month, Hezbollah abducted Elhanan Tannenbaum, an Israeli civilian lured to Abu Dhabi by the offer of a lucrative deal.

In exchange for the three dead soldiers and the release of Mr. Tannenbaum, Israel released more than 430 prisoners in January 2004.

Ian Fisher contributed reporting from Gaza for this article.