HAIFA, Israel — Israel’s war with Hezbollah has not abated since it began last week, with casualties and damage mounting on both sides.

The fighting, which began after Hezbollah killed eight Israeli soldiers and kidnapped two others in a cross-border raid July 12, has killed more than 300 Lebanese and 30 Israelis.

Israeli Tourism Minister Isaac Herzog said Thursday that Hezbollah had fired at least 1,600 rockets into northern Israel since the conflict erupted.

Israeli troops were sent across the Lebanese border Thursday and engaged Hezbollah members firing at Avivim, an Israeli community close to the border. Eight Israeli soldiers were wounded; one Hezbollah gunman was killed.

Hezbollah continued its rocket barrage Thursday, firing some 40 rockets at northern Israel. No casualties were reported.

Sixteen Israeli civilians have been killed by Hezbollah rocket barrages since the conflict began.

Transportation Minister Shaul Mofaz, a member of Israel’s Security Cabinet, told reporters Thursday that Hezbollah’s combat capabilities had been halved. He said Israel should press its offensive in Lebanon until the terrorist group is vanquished.

Israeli officials have said the operation is intended not just to retrieve the captured soldiers but to push Hezbollah back from the border and uproot the thousands of missiles that, with Iranian help, the terrorist group has installed in southern Lebanon and trained on Israeli cities.

Israeli forces have been shelling targets in southern Lebanon and razing former militia outposts, as well as homes that had harbored gunmen and suspected weapons arsenals. Israel also has shelled bridges and airports in Lebanon trying to prevent the transfer of the kidnapped soldiers.

On Monday, an Israeli air strike destroyed at least 10 long-range Iranian-made Zilzal missiles capable of hitting Tel Aviv, according Brig. Gen. Ram Shmueli, the air force’s chief operations officer.

While some countries are calling for an immediate cease-fire, Prime Minister Ehud Olmert told a United Nations delegation Tuesday that Israel would not end its campaign without the release of the kidnapped soldiers and full implementation of U.N. Security Council resolution 1559, which calls for the deployment of Lebanese troops along the border and the disarming of Hezbollah.

The U.N. team, headed by envoy Vijay Nambiar, proposed that the soldier release and cease-fire take place simultaneously.

Olmert’s terms were backed by world leaders at the G-8 summit in Russia over the weekend, who also expressed concern about the crisis, “particularly the rising civilian casualties on all sides and the damage to infrastructure.”

The Bush administration reiterated its criticism Tuesday of Syrian President Bashar Assad, one of Hezbollah’s main patrons, for not doing anything to end the crisis.

Assad is “not doing what he can to create stability, which would be to stop housing terrorist organizations and providing safe haven for them and permitting people to conduct terrorist operations or at least planning on his soil,” White House spokesman Tony Snow said Tuesday.

Assad called for a cease-fire between Hezbollah and Israel in a meeting Wednesday with Turkish Prime Minister Recep Tayyip Erdogan, according to an official Syrian news agency.

Western leaders, led by British Prime Minister Tony Blair, have been pushing the idea of sending a new international peacekeeping force to the region to replace the current, ineffective U.N. force. Speaking at the House of Commons on Wednesday, Blair said Hezbollah must act first to end the conflict.

“This would stop now if the soldiers who were kidnapped wrongly … were released,” he said, according to The Associated Press. “It would stop if the rockets stopped coming into Haifa, deliberately to kill innocent civilians.

“If those two things happened, let me promise … I would be the first out there saying ‘Israel should halt this operation,’ ” Blair said.

Hezbollah has said it will release the captured Israeli soldiers only in a prisoner exchange, but Olmert has ruled out any deal with the terrorist group.

Lebanese Prime Minister Fouad Siniora, who generally has hidden from public view since the crisis began, told an Italian newspaper Thursday that Hezbollah must be disarmed.

Earlier in the week, Siniora had taken a hard line against Israel, calling its attacks a “massacre” and saying he would demand compensation from Israel for damages its attacks had caused.

In remarks published Thursday, however, Siniora criticized Hezbollah for creating a “state within a state” in Lebanon and said “the entire world must help us disarm Hezbollah.” He added in the interview with Corriere della Sera that “It’s not a mystery that Hezbollah answers to the political agendas of Tehran and Damascus.” Later that day, Siniora’s office denied the report, saying he’d been mistranslated. The paper stood by the report, adding that the interview had been recorded.

On the Palestinian front, where Israeli forces have been trying to retrieve a soldier captured June 25 and end rocket fire on Israeli cities and towns, soldiers Thursday killed one Palestinian in the Gaza Strip. Wednesday night, Defense Minister Amir Peretz ordered the closure of the West Bank and Gaza Strip, following two foiled Palestinian suicide bombings and intelligence of more planned.