Israel and Hezbollah forces in southern Lebanon are intensifying their attacks on each other as America and other countries move to impose a U.N.-brokered cease-fire on the warring parties.

Hezbollah mounted its deadliest rocket strike of the current fighting yesterday, killing 12 members of an Israeli army reserve unit near the Lebanese border. Three Israeli civilians also died in Haifa after a flurry of Hezbollah rockets landed on the city.

Israel responded to the attacks on Haifa with a fresh strike against Qana, the Lebanese town where more than two dozen civilians were killed last week in an attack Israel has described as a mistake. Israeli officials said the rockets that landed in Haifa yesterday originated in Qana. At least 14 people were reported killed in Lebanon as a result of yesterday’s fighting.

Both sides seemed to be seizing the opportunity to deliver heavy blows before any cease-fire is implemented. America and France are jointly advancing a U.N. Security Council resolution that calls for an immediate cessation of hostilities.

President Bush is expected to endorse the resolution in unusual public remarks today from his Texas ranch, where he is on vacation. American officials said a vote at the United Nations could come as early as this afternoon.

Lebanese officials, including Hezbollah members in the country’s Cabinet, publicly rejected the proposed ceasefire, saying no cease-fire could be implemented without the immediate withdrawal of Israeli troops from southern Lebanon.

Israeli leaders were noncommittal about the resolution. “We want to remind you that Israel implemented all of the United Nations resolutions concerning Lebanon,” Israel’s vice premier, Shimon Peres, told CNN. “Not that this helped very much, but we kept our respect toward the United Nations.”

In television interviews yesterday, Secretary of State Rice said intense international pressure was being brought to stop the fighting. “Everybody’s been calling for an immediate cessation of hostilities,” Ms. Rice told ABC’s “This Week.” “This is the time now to do it.”

Ms. Rice said she expected the ceasefire to be implemented despite the lack of agreement from Israeli and Lebanese officials. “I think you will see the parties recognize that they have an obligation to respond to U.N. Security Council resolutions,” she said. “I think that the differences here are really not — not really very great.”

Ms. Rice said repeatedly yesterday that the situation would not be allowed to “return to the status quo ante,” a phrase apparently intended to reassure Israel that armed Hezbollah fighters would not be able to remain along Israel’s northern border. However, it was unclear how the cease-fire would be implemented if Hezbollah forces did not abide by it.

The resolution up for debate at the United Nations does not discuss a peacekeeping force to prevent attacks on Israel from Lebanon, but American officials said such a force would be established in another resolution still being developed. While a few countries have offered peacekeepers, none of those offering troops seem to have the stomach for direct combat with Hezbollah.

Ms. Rice did not respond directly to questions about that contingency, but on ABC she said that further fighting by Hezbollah after the cease-fire is declared would signal that “it is not the Lebanese people for whom Hezbollah cares but its own agenda.”

Ms. Rice indicated that she would not press the American-backed Iraqi government to label Hezbollah as a terrorist group — a stance Iraqi leaders have declined to take.

“The European Union hasn’t even stated that,” Ms. Rice said on NBC’s “Meet the Press.” “I think the Iraqi government ought to concentrate on governing Iraq. That’s what they’re trying to do.”

The Israeli Cabinet was told yesterday that the Israel Defense Force captured a Hezbollah terrorist involved in planning and perpetrating the kidnapping of the two soldiers, Ehud Goldwasser and Eldad Regev, that led to Israel’s retaliation.

Elsewhere, Israeli forces detained the speaker of the Palestinian Arab parliament at his home in the West Bank. Aziz Dweik, a leading member of Hamas, was held after 20 Israeli vehicles surrounded his home in Ramallah, the BBC reported.

The Israeli military said Mr. Dweik was a legitimate target. However, the Palestinian Arab prime minister, Ismail Haniyah, condemned the action as an act of “piracy.”