President Bush arrives Friday in the historic Russian city of St. Petersburg for the annual summit of the industrialized nations known as the Group of Eight, a gathering that President Putin, at least, had hoped would repair fraying political relations between America and Russia, and also strengthen economic channels between the two countries.

But both men found themselves scrambling yesterday to deal with an entirely unexpected item that’s now certain to appear in the agenda for the summit, which runs July 15–17 at the sprawling 18th-century Konstantinovsky Palace.

That item, of course, is the widening conflict in Lebanon, which pits Israel against the Islamic terrorist group Hezbollah. It is no secret that the Russian president enjoys far more cordial relations with many militant leaders in the Middle East than with Israelis. It is also no secret that he wants to play a more meaningful role in the region.

Will his fellow G8 leaders invite his assistance? A preliminary reading of the diplomatic tea leaves suggests that his moment in the sun at the only G8 talkfest he will host before his two presidential terms expire in 2008 may not be luminous.

“The history of these so-called economic summits is that almost always politics dominates, and this year will be no exception,” the president of the Council on Foreign Relations, Richard Haass, told The New York Sun last night. “What’s remarkable is the number of political issues before the leaders — from Lebanon to Iran to North Korea to Iraq and Afghanistan. The summit participants will have their hands full, and then some.

“What adds to the difficulty is that many of the principal leaders at the summit are already in a weakened position. Mr. Bush has his difficulties. Prime Minister Blair of Britain is having his domestic political problems. Japanese Prime Minister Koizumi is leaving office soon. Interestingly, one effect will be that what many thought was going to be the dominant issue — Russia and its internal situation — will probably be pushed to the back burner,” Mr. Haass said.

That will come as a relief to the host. While Mr. Putin enjoys unprecedented popularity in his country of 143 million people, there is growing concern in the Bush administration and in the international community over the Russian state’s draconian interventions in the domestic economy, attacks on press institutions, widespread bureaucratic corruption, and backtracking on systemic reforms that began shortly after the collapse of the Soviet Union in December 1991.

Mr. Putin’s campaign to eliminate all challenges to his authority is worrisome to Western supporters of democracy. They are troubled by the closing down of independent television networks, the elimination of elections for regional governors, and the jailing of oil tycoon Mikhail Khodorkovsky in October 2003 and the subsequent destruction of his private company, Yukos. In addition, Western critics say, Russia’s record on human rights isn’t terribly encouraging.

Beyond the current situation in Russia, two questions raise themselves: If Mr. Putin continues to consolidate power in the presidency, what about the traditional system of power-sharing between the executive, legislative, and judicial branches in a democratic system based on adult franchise?

Second, who will succeed Mr. Putin when he leaves office? Will Mr. Putin relinquish office readily? Will he install a puppet and then act as the power behind the presidential office?

Despite the concerns over the domestic situation in Russia, the irony is that there is a convergence between Russia and America on several issues. They include nuclear nonproliferation, cracking down on terrorism, bilateral strategic force parity, and oil and gas.

“But these common interests come under a cloud because of Mr. Putin’s consolidation of federal power,” the director of the Center for Transition Economies at Columbia University, Padma Desai, told The New York Sun. “Because things seemed to be going so well under Putin’s predecessors, Gorbachev and Yeltsin, many observers find today’s situation difficult to grasp.

“The big macro question between the U.S. and Russia is: How high a price are we willing to pay in terms of turning a blind eye toward repression in Russia in exchange for using Mr. Putin’s good offices for problems that aren’t in our control — such as Lebanon, Iran, North Korea, and the Hamas militants who rule the Palestinians,” Ms. Desai, who is the Harriman Professor of Comparative Economic Systems, said.

What she terms the “big macro question” may come up only implicitly at the summit. Certainly, the 10,000 visitors who are expected to descend on St. Petersburg, a city of 4.7 million people — and the hometown of Mr. Putin — will not be privy to informal deliberations.

Some of the visitors will include critics of the G8 summit process itself. And some of the critics — such as Mr. Haass — contend that the G8 is an anachronism.

“It has a structural problem — as with the United Nations Security Council,” Mr. Haass said. “What you have are institutions that were created in one geopolitical era, and that wouldn’t be invented or created in the same form were they launched today. The question now is how do we adapt or complement them, or replace them?”

Mr. Haass is among a growing number of influential scholars and policy analysts who believe that the G8 must include China and India.

“These are rising economic powers that are also growing political voices regionally in Asia and globally,” he said. “To the extent that the G8 is meant to manage both political and economic issues, it has simply too much of a European presence, and not enough of an Asian one.”

The G8 members — America, Britain, Canada, France, Germany, Italy, and Japan — account for nearly 67% of the world economy, which is $44 trillion. Meanwhile, China and India have registered such impressive economic growth that within a decade their economies are expected to be larger than those of all of the U.N.’s 191 member countries other than America.