A member of Hamas was reported killed in an airstrike Friday, less than 24 hours after Israeli troops and Palestinian militants had waged their most intense battles since Israel re-entered the Gaza Strip last week to secure the release of a captured soldier and stop rocket fire into Israel.

The death toll had risen throughout Thursday in sometimes fierce fighting involving everything from rifles to airborne missiles.

It was one of the bloodiest days in Gaza since the uprising began in 2000. The death toll varied and the Palestinians provided no official figures. The Associated Press counted at least 21 dead Palestinians, and Reuters 19. One Israeli soldier was reported killed by a sniper. Reuters reported Friday that the militant was killed after an Israeli plane fired at four armed men near the scene of the worst violence from the day before.

Most of the deaths Thursday were in northern Gaza, where after days of sporadic clashes Israeli forces moved south from the destroyed former Israeli settlements to the outskirts of Beit Lahiya. There, in the northwest corner of Gaza, Palestinian fighters had been preparing earthen barricades, explosive charges and positions for shooting.

Israel's defense minister, Amir Peretz, said that although Israel pulled out of Gaza last year, "no one should see that as a guarantee that we cannot reach territory in which we feel we have no choice but to operate."

Heavy fighting erupted in and around Beit Lahiya, especially in the western neighborhoods of Atatrah and Salatin near the sea, with Palestinian militants using light weapons like Kalashnikovs, M-16's and antitank grenades, fighting running battles with Israeli troops in armored personnel carriers, modern tanks and armored D-9 bulldozers.

Palestinians were seen planting explosives in manholes, hoping to blow up a vehicle as it drove by. One masked fighter rode away on a bicycle after laying such a charge, a spool of electrical wire unrolling from the back of his bike.

Israeli tanks fired shells at houses where Palestinian fighters sheltered, and soldiers fired at groups of armed Palestinians who fought in the streets, sometimes surrounded by curious and excited children. At times, Israeli soldiers fired near groups of children in what appeared to be an effort to get them to scatter.

The Palestinian interior minister, Said Siam, who is responsible for most of the security services, declared a state of emergency. His spokesman said the minister "called on all Palestinian security and military services to participate in the moral, national and religious duty to defend our people."

The Palestinian prime minister, Ismail Haniya, called on Arab and international groups to help the Palestinians and to press for an end to the Israeli offensive.

"Solving issues can't be through military escalation or expanding their scope, but through stopping the aggression, and respecting the will of the Palestinian people and answering to their just nationalist demands," Mr. Haniya said.

Three separate airstrikes accounted for the deaths of six Palestinians near Beit Lahiya. The Israeli military said all six were gunmen, while Palestinian officials, medical workers and witnesses gave conflicting information on how many were militants and how many were civilians.

In the same area, gunmen from various Palestinian factions fired automatic rifles and antitank rockets at the Israeli troops. Israeli tank fire killed two militants, Palestinians and the Israeli military reported.

About 30 Palestinians were wounded in the Beit Lahiya area, according to the Palestinian medics.

Also, an Israeli soldier was shot in the head and killed in Beit Lahiya, apparently by a sniper, the military said. The Popular Resistance Committees, a faction of gunmen from various groups, claimed responsibility. A second soldier was wounded in the area, the military added.

Before dawn, a Hamas militant and a Palestinian policeman were killed in an Israeli aerial attack on a beach in northern Gaza, the Palestinians and the Israelis said.

In southern Gaza, an Israeli airstrike killed two militants from Islamic Jihad in Abasan, near the southern town of Khan Yunis, Palestinian witnesses and security officials said. The men were firing an antitank rocket at Israeli tanks and troops positioned there.

Israel's military has re-entered both the north and the south of Gaza for what it says is a two-pronged mission.

In the south, the troops were sent in shortly after Cpl. Gilad Shalit, a tank gunner, was captured just inside Israel by militants and taken to Gaza on June 25. Ghazi Hamad, a spokesman for the Palestinian Authority, said the sides should seek a diplomatic solution that would lead to Corporal Shalit's release.

"We don't want Gaza destroyed, nor do we want attacks," Mr. Hamad told Israel radio. "And you want him to return to his family."

However, Israel says it will not negotiate for the release of the soldier, and has rejected Palestinian demands that large numbers of Palestinian prisoners be freed.

The militants have at various times demanded that all women and youths held by Israel be released, and they have also said that 1,000 prisoners of various nationalities must be freed. But the militants, and Hamas leaders, say that the corporal should not be released without some kind of Israeli prisoner release in return.

The Arabic-language newspaper Al Hayat, which is based in London, reported Thursday that militants had revised their demands, saying that Corporal Shalit could be freed if all Palestinian women are released from Israeli jails along with 30 men who are serving long-term sentences. There was no independent confirmation of that report.

The Israeli military said Palestinians fired eight rockets from Gaza at Israel on Thursday, but only four made it into Israeli territory and none caused injury. Three apparently landed inside Gaza and one fell in the sea, the military added.

In the north, Israeli troops began edging into the territory on Monday with the aim of preventing Palestinian rocket fire on southern Israel.

But until Thursday, the armored forces, consisting mostly of tanks and armored personnel carriers, had ventured only about half a mile into northern Gaza, remaining outside the Palestinian towns, and there was only occasional shooting.

As the Israeli troops moved on Beit Lahiya on Thursday, the fighting quickly escalated. Israeli tanks also entered three former Israeli settlements on the northern edge of Gaza that were evacuated last year.

Israeli Prime Minister Ehud Olmert and his aides have said the current offensive is not an attempt to reoccupy Gaza. But Mr. Olmert, along with some political and security officials, has urged the Israeli public to be patient and suggested that the operation could be quite lengthy.

Over all, nearly 20 Palestinians have been killed since the Israeli incursion began, most of them militants.

Steven Erlanger reported from Beit Lahiya for this article, and Greg Myre from Jerusalem.

Copyright 2006 The New York Times Company