U.S. Secretary of State Hillary Rodham Clinton meets with Russian Foreign Minister Sergey Lavrov, in St. Petersburg, Russia, June 29, 2012. (POOL/Reuters)

If Russia holds the key to ending the conflict in Syria, as the Obama administration and much of the world have long said it does, then why won’t it open the door to a solution?

Moscow has said it will not abandon its longtime material and moral support for President Bashar al-Assad just because the United States and other powers have ganged up on him. The Russians say they are acting out of respect for Syrian sovereignty and concern about who would replace Assad.

Western officials and Russia experts have suggested additional reasons. They contend Russia fears losing a base of influence in the Middle East, a Mediterranean naval harbor and a reliable customer for its defense industry. Moscow also worries about Islamic extremists within the Syrian opposition and may be playing a Cold War-style game of one-upmanship and enjoying the international spotlight, they said.

But for the broad coalition of countries that want to see Assad gone and an end to a conflict that has left thousands of civilians dead, there is no satisfying explanation for a policy whose eventual downsides seem blindingly obvious.

“If you look at everything they claim to care about — stability, economic ties, a military and defense relationship — all of that presumably will go away if Syria crumbles into either a failed state or a prolonged sectarian conflict,” said Andrew S. Weiss, a Russia expert who served in the Bill Clinton administration.

With another meeting of world powers about the 15-month crisis scheduled for Saturday in Geneva, the Obama administration believes it has detected some weakening in Russia’s steadfast refusal to jettison Assad. Officials said they also see signs of interest in new proposals from U.N. envoy Kofi Annan for a transition government of national unity, which will debated in Geneva.

“They have indicated that, to them, the issue is not some personal commitment to Assad,” said a senior administration official, who spoke on condition of anonymity because of diplomatic sensitivities. “There is a lack of understanding about what comes next, but the implicit suggestion is that they are open to a discussion that could include Assad leaving.”

Secretary of State Hillary Rodham Clinton stopped in St. Petersburg on Friday to confer with her Russian counterpart, Foreign Minister Sergei Lavrov, before they travel to Geneva.

Accounts of their meeting were cryptic and contradictory. Lavrov told reporters that the two agreed on “most things” and said: “I felt Hillary Clinton’s position has changed. She understands our position.”

A senior State Department official in St. Petersburg told Reuters news service, “There are still areas of difficulty and difference.”

According to Russia’s Interfax news agency, there was no progress at a preparatory session in Geneva on Friday attended by representatives from Washington, Moscow and other U.N. Security Council and Arab League members. “Russian delegates stopped other countries’ representatives from reaching a consensus on implementation of Annan’s plans,” the report said.

A statement from Russia’s Foreign Ministry said that it viewed the upcoming ministers’ gathering as a “positive step,” but that Russia was “not changing its principled approach that Syrians should determine the future of their country themselves.”

In a separate statement, the ministry observed that Annan’s decision to hold the meeting without inviting Iran, Saudi Arabia and other countries in the region “does not seem sensible.”

Annan’s new proposals have been described by participants as a last-ditch effort to achieve international consensus, spurred by rapidly deteriorating conditions in Syria. Many are pessimistic that Russia has decided on a policy change, noting that previous optimism has proved unfounded.

After British Prime Minister David Cameron said Russian President Vladimir Putin was “explicit” at this month’s Group of 20 summit in Mexico “that he does not want Assad remaining in charge in Syria,” Putin publicly indicated he had said no such thing. When French President Francois Hollande suggested at the summit news conference that Assad could seek exile in Russia, Putin countered that Assad might be more comfortable in France.

Following their own G-20 talks, Putin and Obama issued a joint statement calling for ”immediate cessation of all violence” in Syria and support for Annan’s efforts. “We are united,” it said, “in the belief that the Syrian people should have the opportunity to independently and democratically chose their own future.”

But reports from their closed-door session, which administration officials said was dominated by Syria, indicated that the two leaders did not necessarily find the same meaning in those words.

So far, Moscow has not linked disagreement over Syria to other issues in the U.S.-Russia relationship. “Their hard line is just on Syria,” the senior administration official said. “They haven’t sought to leverage missile defense or the NDN as part of the Syria discussions.” The NDN refers to the Northern Distribution Network, the transit route through Central Asia and Russia being negotiated for U.S. and NATO forces and equipment leaving Afghanistan.

But Putin does not appear to see Syria as a useful issue for promoting bilateral cooperation.

“He’s waiting to see who wins the [U.S.] election before he decides what Russia’s U.S. policy is going to be,” said Olga Oliker, a senior policy analyst at the Rand think tank. “Why make all sorts of compromises? He doesn’t think he can influence the election, [but] he wants to see what happens.

“Russians get a lot out of the status quo right now,” Oliker added. “It’s very unfortunate what’s happening in Syria, but if you’re Russia, it could be worse. ‘We’re still the center of attention, we still have the capacity to influence the situation . . . we’re standing up for things we believe in,’ which looks good at home as well.”

Beyond the speculation and Russia’s stated reasons, Weiss said, “The roots of Russian support for Assad remain very murky, even to experts.”

Weiss is among the pessimists about a Russian change of position. “Most of the shifts they’ve made to suggest possible outcomes where Assad doesn’t survive look mostly like rhetoric not backed up by firm action,” he said.

“If they were serious, they would be doing things to curtail arms shipments and other support, including financial. There is no indication that where it matters the Russians have changed their tune.”

Will Englund contributed to this report from Moscow.