There's little sign of a ceasefire between Israel and Hizbollah guerrillas. Israeli forces fought Hizbollah in south Lebanon on Tuesday (July 25) and kept up two weeks of air strikes. Hizbollah fired more rockets into Israel. Smoke could be seen rising above the Lebanese coastal city of Tyre as more victims were taken to the hospital morgue. Hizbollah said five guerrillas died in the past two days. Israel reported two soldiers killed on Monday (July 24) but said it had inflicted dozens of casualties on Hizbollah. An Israeli air strike killed a family of seven, Lebanese security sources said. The raid on the village of Nabatieh killed a man, his wife and five children, the sources said. The air strike brought to 390 the number of people killed in Lebanon during nearly two weeks of conflict. The majority of those killed have been civilians. Hizbollah has killed 41 Israelis since the conflict was triggered on July 12 by the guerrilla group's capture of two Israeli soldiers. Meanwhile, residents in Beirut took to the street demanding an end to Israel's military campaign. The protesters marched to the governmental palace, where the cabinet is based. They then moved on to the United Nations building. The crowd pledged support for Hizbollah and its leader Sayyed Hassan Nasrallah. Israeli Prime Minister Ehud Olmert agreed on Tuesday to allow aid airlifts to Lebanon but said he was determined to pursue an offensive against Hizbollah. After talks with U.S. Secretary of State Condoleezza Rice, Olmert said both agreed resolving the crisis must include disarming Hizbollah, its removal from Israel's border and deploying an international force to ensure it cannot menace the Jewish state. Rice, who spelled out the truce terms to Lebanese leaders during a visit to bomb-battered Beirut on Monday, said it was time for a "new Middle East". Rice has made clear she is not seeking a quick ceasefire and that any solution should address the root causes of the conflict -- for which Washington and Israel blame Hizbollah and its backers in Iran and Syria. Israel's army, which has also waged a military campaign in Gaza since June 28 to recover a soldier seized by Palestinian militants, believed it may have a week to keep pounding Hizbollah before a deal was reached, security sources said.