ST. PETERSBURG, Russia – The Bush administration made clear yesterday that it saw the crisis in the Middle East as an opportunity for the world to deal once and for all with Hezbollah and to rein in its sponsors, Iran and Syria.

As the conflict moved into its fifth day, it was increasingly apparent that Washington was willing to give Israel its support in its military campaign in the hope that it would finally extinguish the threat posed by America’s old enemy, the Iranian-backed Shiite group.

In an attempt to counter the charge that America had been too uncritical of Israel’s military action, President Bush’s aides stressed their concern yesterday for civilian casualties and worries over damage to infrastructure.

But they ruled out the idea of calling for a cease-fire, arguing that it would be a short-term measure that would only be followed by more attacks by Hezbollah.

Rather the time was ripe for a long-term solution, with the keys being the disarmament of the radical Shiite group and unspecified consequences for two of America’s oldest Middle Eastern foes, Tehran and Damascus. In short, they say, it is time “to drain the regional swamp of extremism.”

“This is a complex time, a worrying time, a time of great concern about the toll on civilians,” Secretary of State Rice said. “It is also a time when we have an opportunity to lay a foundation … for a permanent cessation of violence.”

The unofficial American strategy seems to be to rely on a combination of “muscular diplomacy” and Israeli military might.

The Bush administration bolsters its argument by citing the need finally to realize the outstanding goals of U.N. resolution 1559, which calls for the disbanding of regional militias. White House aides say several key regional leaders have the same aspiration, born of the desire to rein in Iran’s regional network.

One of the principal worries for America is that the Israeli forces will be so heavy-handed that they hand a diplomatic victory to their opponents.

Ms. Rice said American officials had stressed to Israel the need for restraint and also the risk of undermining the fledgling democratic government in Lebanon. But she refused to be drawn when asked if America had a “tipping point” at which civilian casualties would no longer be acceptable.

Reprising the Bush regional philosophy, she sought to present the crisis as the fruit of years of international failure to rein in “extremists.”

“We are at an important juncture right now because extremists have showed their hand. And they’ve showed that their sponsors are in Tehran and in Damascus. Things are clarified right now,” she said.

Administration hawks see this as a key moment in the protracted showdown with Iran. Officials in Washington have been growing frustrated at the failure of diplomatic efforts to quash Iran’s nuclear ambitions.

With 130,000 American troops bogged down on Iran’s border, and America’s motives in the region regarded with huge suspicion following its push for the war in Iraq, Ms. Rice has persuaded Mr. Bush that the American hawks have to be held in check.

But now, the Bush administration sees a dual opportunity to intensify the pressure on Iran. Last night it appeared that America was winning support in its bid to use “muscular diplomacy” backed up by Israeli might to punish Hezbollah. France, a traditional power broker in Lebanon, also cited the need to realize resolution 1559.

But securing support to punish Damascus and Tehran will be far harder, as was clear in the G-8 summit statement on the crisis last night.There was no explicit reference to Syria or Iran. It cited only the threat posed by “those that support” extremist elements.