After one of the most violent days of Israel's nearly three-week-old war against the Hamas movement in Gaza, the conflict appeared late Thursday to be moving toward a diplomatic solution.

Just before midnight, Foreign Minister Tzipi Livni unexpectedly flew to Washington, where she and U.S. Secretary of State Condoleezza Rice were expected to sign an agreement on measures intended to stop Hamas from smuggling weapons into the Gaza Strip from Egypt, a critical Israeli demand. Meanwhile, Israeli officials said they were hopeful that an Egyptian-brokered cease-fire with Hamas was within reach.

Israel's two other top leaders, Prime Minister Ehud Olmert and Defense Minister Ehud Barak, met Thursday night, discussing terms to which Hamas had agreed in principle on Wednesday. Although there were no announcements after the meeting and the talks still had the potential to sour, officials said the gap between Israel and Hamas had narrowed considerably. Israel's top negotiator, Defense Ministry official Amos Gilad, was scheduled to return to Cairo on Friday for more talks.

The two sides are discussing a one-year renewable truce, said a senior Israeli official, declining to be identified by name because of the sensitivity of the talks. The agreement would specify how quickly Israel would withdraw its forces from Gaza and when it would reopen border crossings, the official said. Israel has demanded guarantees that the rocket fire from Gaza will stop.

Fighting continued amid the diplomatic activity. In past wars, Israel has intensified its military campaign in the final days and hours before a cease-fire in order to achieve favorable truce terms.

Dozens of Palestinians died Thursday, bringing the toll to more than 1,090, according to Palestinian health officials. A Gazan Health Ministry official, Muawiyah Hassanein, said 375 children, 150 women and 14 medical staffers were among the dead. He said 5,000 people had been injured. Thirteen Israelis have been killed, including three civilians.

As Israeli troops backed by helicopter gunships pushed into densely populated Gaza City, a U.N. compound and a hospital building were shelled and a Hamas leader was killed.

At the U.N. compound, an Israeli shell ignited a warehouse filled with food and injured three people. U.N. Secretary General Ban Ki-moon -- in Israel to push for the cease-fire -- said Barak had initially apologized for the incident, calling it a "grave mistake." But Olmert, while expressing regret, later said a Hamas fighter had used the building to take cover after firing at Israeli troops.

U.N. Relief and Works Agency spokesman Christopher Gunness vehemently denied that charge, saying it was another in a series of incidents in recent weeks in which Israel has made excuses for striking U.N. facilities and personnel. "Their credibility is hanging in rags," he said.

Gunness also accused Israel of hitting the U.N. compound with white phosphorus, a weapon that under international law is not supposed to be used in urban areas because it is highly flammable. Israel has not commented on its possible use of white phosphorus but has insisted it is in compliance with international law. White phosphorus is permitted for use in illumination and in creating smoke screens.

Separately, an artillery shell hit a hospital's administrative building. The building caught fire, trapping workers inside, hospital officials said. An Israel Defense Forces spokesman said the military was investigating.

"For two hours the fire was burning, with heavy smoke," said Ziad Kahlut, a doctor at al-Quds Hospital. "We were panicked that the fire would spread to the rest of the hospital."

Although that did not happen, Kahlut said conditions at the hospital were grim. "Our hospital is now overcrowded with the sick, the wounded, staff and some 300 civilians, many of them women and children, who are taking shelter," he said. "I do not know how long this can last."

Also on Thursday, a senior Hamas leader, Interior Minister Said Siam, was killed when an Israeli airstrike flattened his brother's home in the Jabalya refugee camp, according to an Israeli military statement later confirmed by Hamas. Siam was one of Hamas's top five leaders within Gaza, with leadership over a 13,000-member police and security force, and was considered a hard-liner who resisted compromise with Israel. Siam's brother and other Hamas members were also killed.

Siam is the highest-ranking Hamas political leader to die in the 20-day Israeli campaign; the others are believed to have gone into hiding.

Hamas and its allies in Gaza fired more than 25 rockets into Israel on Thursday. There were no immediate reports of injuries.

Thursday's urban combat forced anxious residents to flee their homes, while others reported being trapped, too terrified to move. The skyline was obscured by black smoke rising from several high-rises in the heart of Gaza City that had been struck by artillery shells, as well as by smoke screens being dropped from helicopters.

Witnesses said Israeli soldiers were moving through the southwestern neighborhood of Tel Hawwa. "For 12 hours we were under continuous bombing, from 1 a.m. to 1 p.m.," said Fathi Sabah, a journalist working for the London-based Arabic-language newspaper al-Hayat.

At one point, he said, his building was struck and a fire broke out. Firefighters were unable to get through. "We had to try to extinguish the fire with the few pots of drinking water we have," said Sabah, who endured the shelling with his two daughters, Rima, 12, and Jumana, 11 . "We were just waiting to die. It was hell."

Among other buildings hit Thursday was a high-rise used by journalists. Two cameramen were injured.

At a news conference in Tel Aviv, Ban said that civilian suffering in Gaza had become "unbearable" and that the territory was facing "a dire humanitarian crisis."

Livni defended the military offensive, saying Israel is "doing what it needs to do to defend its citizens."

Hamas and its allies have fired thousands of rockets into Israel in the past eight years. The pace accelerated after the Islamist movement, which won Palestinian elections in 2006, routed forces loyal to the rival Fatah party in June 2007 and seized control of the narrow coastal strip. Since then, Israel has implemented a crushing economic blockade and carried out regular military raids that it has said were a response to rocket fire.

Hamas's 1988 charter calls for Israel's destruction, but current leaders say they are willing to enter into a long-term truce with the Jewish state.

Israel has not allowed foreign journalists into Gaza to operate independently since it launched its offensive Dec. 27. On Thursday, a small group of journalists was allowed to travel into Gaza with the Israeli military.

In an interview, an Israeli sergeant, 20-year-old Almog, told the reporters that Hamas's resistance had been less than expected. "They are villagers with guns. They don't even aim when they shoot," said Almog, a gunner on an armored personnel carrier who was not allowed to give his last name. "We kept saying Hamas was a strong terror organization, but it was more easy than we thought it would be."