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Leaders of the world's wealthiest nations agreed Sunday that three Israeli soldiers kidnapped by terror groups must be returned as a first order of business, and that all sides must put down their arms to resolve a conflict that is tearing up both Lebanon and Israel's northern region.

Members of the Group of Eight, the world's industrialized nations and Russia, issued a consensus statement that they say sends a "strong message" on the Mideast crisis.

The joint statement also says terrorist groups in the region cannot be allowed to plunge the Middle East into chaos and must immediately halt their attacks. It also calls on Israel to cease its military operations and withdraw from Palestinian-controlled Gaza.

"The immediate crisis results from efforts by extremist forces to destabilize the region and to frustrate the aspirations of the Palestinian, Israeli and Lebanese people for democracy and peace," the statement reads.

"These extremist elements and those that support them cannot be allowed to plunge the Middle East into chaos and provoke a wider conflict. The extremists must immediately halt their attacks. It is also critical that Israel, while exercising the right to defend itself, be mindful of the strategic and humanitarian consequences of its actions. We call upon Israel to exercise utmost restraint," the statement continues.

G8 leaders took a group photo in front of the Konstantinovsky Palace in St. Petersburg and held a working dinner there. Beforehand, however, they expressed deep concern over the Mideast situation, particularly the rising number of civilian casualties on all sides and damage to infrastructure.

But the joint statement does not mean that all sides are in agreement over responsibility for the latest round of violence, which began after Hamas militants crossed a security border and kidnapped 19-year-old Israeli Cpl. Gilad Shalit on June 25.

On Wednesday, Hezbollah got into the act by kidnapping two Israeli soldiers in a cross-border operation. Israel responded by strategically striking Lebanon's highways, Beirut's airport tarmacs and southern electricity pumping stations. The terror group struck back at Israeli cities and on Sunday fired a relentless barrage of rockets into the Israeli city of Haifa, dramatically escalating the conflict.

Israel responded late Sunday with an attack on Tyre, in southern Lebanon. In all, more than 130 civilians on both sides of the fight have been killed.

Russian President Vladimir Putin suggested early Sunday that Israel "is pursuing wider goals" in its military campaign against Lebanon than the return of its two captured soldiers from Hezbollah. He did not say at his midnight news conference what those goals might be.

French President Jacques Chirac said more must be done to end actions jeopardizing the security of Lebanon, which includes Israeli attacks as well as actions by Syria and Lebanon.

But U.S. President George W. Bush said the latest incident has revealed a "moment of clarification" in which the world can see that Hezbollah is deliberately trying to disrupt the peace process with the help of rogue states.

"One of the interesting things about this recent flare-up is that it helps clarify a root cause of instability in the Middle East, and that's Hezbollah and Hezbollah's relationship with Syria, and Hezbollah's relationship to Iran and Syria's relationship to Iran; therefore, in order to solve this problem it's really important for the world to address the root cause," Bush said.

German Chancellor Angela Merkel appeared to agree.

"We do not want to let terrorist forces and those who support them have the opportunity to create chaos in the Middle East; therefore we place value on clearly identifying the cause and effect of events," she told reporters.

Merkel said the leaders believe that "first of all, that the Israeli soldiers must be returned unharmed, that the attacks on Israel must stop and that then, of course, also the Israeli military action must be ended."

Chirac insisted that the G8 statement calls for a ceasefire and noted that the text of the G8 statement says the "most urgent priority" is to create the conditions for ending the violence.

But Bush did not take the position that the G8 is going to demand Israel agree to a ceasefire, which has been a demand of Lebanese Prime Minister Fuad Siniora. Secretary of State Condoleezza Rice said to do so would not solve the underlying problem.

"What we have asked of the Israelis is that they act in a way to avoid innocent civilian casualties, to avoid the destruction of civilian infrastructure, because there does need to be another day. Israel will need to have those moderate allies in Lebanon and in the Palestinian territories in order to create a stable peace," she told FOX News.

"But what we don't want to do is to have a cessation of violence that is not going to last for more than the next time that Hezbollah or Hamas decides that they're going to launch a rocket into Israel or abduct an Israeli citizen," she said.

Rice added that past U.S. administrations, Republican and Democratic, have placed stability ahead of democracy in the Mideast and gotten neither. That false stability contributed to the rise of Al Qaeda.

"What is really happening here is that extremists have revealed their hand. They are demonstrating that they cannot tolerate the forward march of democratic moderate forces in the Middle East.

"They are trying to destabilize the young government of Lebanon by, in the case of Hezbollah, using Lebanon's territory to attack Israel without the knowledge of the Lebanese government, and of course, they're doing this in conjunction with sponsors in Damascus and in Tehran," Rice said.

Still, Connecticut Democratic Sen. Chris Dodd, a potential 2008 presidential contender, said this administration has not done enough to engage enemies diplomatically.

"For Israel's benefit and our own, we have missed, I think, over the last number of years the ability to really engage in the kind of diplomatic efforts in the Middle East. From 1967 up until the end of the Clinton administration, every administration has remained very, very engaged in the Middle East. This administration, unfortunately, has seen the word diplomacy and negotiation as somehow a favor to your enemies," Dodd told FOX News Sunday's Chris Wallace.

Despite that argument, and any impact the latest crisis could have on November's midterm election, some in Washington continue to assert Israel's right to defend itself.

"U.S. policy should be number one, stand with your friend. Israel's a wellspring in the wilderness. And any country, particularly Israel, has a right to defend itself and protect its citizens as we do," said Virginia Republican Sen. George Allen, also a possible 2008 presidential candidate.

Bush has urged Israel to exercise restraint in its military actions. The G8 statement published by the United States, Russia, Japan, Germany, Britain, France, Italy and Canada also offers full support to the United Nations mission in the region.

"We extend to the government of Lebanon our full support in asserting its sovereign authority over all its territory in fulfillment of [U.N. Resolution 1559]. This includes the deployment of Lebanese Armed Forces to all parts of the country, in particular the South, and the disarming of militias. We would welcome an examination by the U.N. Security Council of the possibility of an international security/monitoring presence," reads the statement.

The U.N. Security Council adopted Resolution 1559 in September 2004, calling for the disarmament of all militias and strict respect for Lebanon's sovereignty, territorial integrity, unity and political independence.

Merkel said that the leaders are "convinced that the government of Lebanon must be given all support and that the relevant U.N. resolutions regarding the south of Lebanon must also be implemented, and we also demand that in addition to the U.N. activities, another observation and security mission is established. That must be worked out through the U.N."

The statement also calls for the Palestinians and Israelis to return to the peace plan envisioned in the "road map" for Mideast peace and compliance with applicable U.N. Security Council resolutions.

FOX News' Bret Baier, Wendell Goler and Rudi Bahktiar and The Associated Press contributed to this report.