US President Barack Obama opened his first Moscow summit with confidence on Monday, predicting "extraordinary progress" out of meetings set to test his diplomatic skills on important priorities such as nuclear arsenal reductions and the fight in Afghanistan."The United States and Russia have more in common than they have differences," Obama said he sat down in an ornate Kremlin room with Russian President Dmitry Medvedev. "If we work hard in these next few days ... we can make extraordinary progress that will benefit the people of both countries."With both men eager to reset damaged relations, Obama's host launched the high-stakes summit with similar good will."We'll have a full-fledged discussion of our relations between our two countries, closing some of the pages of the past and opening some of the pages of the future," Medvedev said, through a translator. "It is my hope that it will be possible to tackle successfully" a range of problems from the economy to security and energy and the environment.The first US-Russia summit since the early part of the George W. Bush presidency presents a challenge for Obama, with Russia home to a wary public, a two-headed leadership and lingering hard feelings. What much of the world will watch are signs of Obama's relationship with Russia's two leaders, Medvedev and his mentor, Prime Minister Vladimir Putin.The foundation set now could affect how much cooperation Obama gets in areas in which the US needs help from Russia - chiefly pressuring Iran and North Korea to give up their nuclear weapons ambitions, but also in tackling terrorism, global warming and the economy.Both sides talked going in of improving ties and of the importance of early results.Agreements negotiated ahead of time give Obama something to take home before the summit even got under way, including another step toward the world's two largest nuclear powers scaling back their arsenals and agreement from Russia to let the United States use its territory and air space to transfer arms into Afghanistan for the forces fighting extremists there.Other side agreements meant to sweeten the talks included a new joint commission to try to account for missing service members of both countries dating back to World War II. Four working groups will look into missing military personnel from World War II, the Korean War, the Vietnam War, the Cold War and Soviet military personnel still missing from Moscow's 10-year occupation of Afghanistan.The White House also said that the two countries have agreed to cooperate in the fields of public health and medical research, an arrangement intended to range across public health issues from infectious diseases to promotion of healthy lifestyles to improving global health.Yet, the two sides remain in a stalemate over the US pursuit of a missile-defense system in Europe. Obama's administration is reviewing the efficacy of plan, which Bush had pushed hard.US leaders have been hopeful of receiving Russian cooperation on missile defense. But both sides have also shown signs that they are hardening their positions ahead of the summit.The basic problem is unchanged: The US contends the program is designed to protect US allies in Europe from a potential nuclear attack by Iran, but the Russians see it as a first step toward a system that could weaken their offensive nuclear strike potential."We're going to have to work our way through that," Adm. Mike Mullen, chairman of the U.S. Joint Chiefs of Staff, told "Fox News Sunday."Obama's distinctive Air Force One jetliner touched down with drizzly gray skies blanketing Moscow. He continued down a formal reception line on the airport tarmac, introducing his wife, Michelle, and their two daughters to the Russian officials waiting to greet them.The entourage then headed directly to a wreath-laying ceremony at Russia's Tomb of the Unknown Soldier, brilliant sun breaking over the city's center through the days of clouds as they drove in. The president walked slowly behind three high-stepping Russian soldiers, then straightened the wreath's ribbon where they placed it in front of the eternal flame and stood alone briefly.The summit starts a weeklong trip for Obama that also features G-8 meetings and a visit with the pope in Italy, and a speech in Ghana.Obama's mission in Moscow is two-pronged, divided over two days. Building ties and inking security and cultural deals with the leadership comes first. He will also devote a prominent amount of time to leaders of Russia's civil society to help those relationships, too.There is plenty of room for improvement. Obama, who has enjoyed adoring crowds in travels across Europe so far, will face a skeptical Russian population, polling out Sunday shows.Only 23 percent of Russians have confidence in Obama to do the right thing in international affairs, according to the University of Maryland's WorldPublicOpinion.org. Just 15 percent of the Russians polled said the U.S. is playing a positive role in the world; most said the United States abuses it power and makes Russia do what the U.S. wants."I would like there to be real change, not just talk," said Valentina Titova, a 60-year-old retired economist strolling not far from the Kremlin. "I would like to see American meddle less in other countries. They think they're so superior to others, they put themselves on a pedestal."Aiming to change attitudes, Obama will outline his vision for US-Russian relations at a speech at the New Economic School. It is unclear how many people will see it. Russian leaders control the television outlets.The dominant theme of the summit is security, and Obama and Medvedev are set to announce progress toward renewing a strategic arms reduction pact that expires in December. The eventual deal could cut warheads from more than 2,000 each to as low as 1,500 apiece."At the moment I think we are all moderately optimistic, both the Russian side and the American side, so far as I know," Medvedev said ahead of Obama's arrival in an interview with Italian news outlets.As Obama told a Russian-language news channel in the days before the summit: "America respects Russia. We want to build relations where we deal as equals."Yet he also caused a stir in Russia by telling The Associated Press last week that Putin has to learn that "the old Cold War approaches to US-Russian relations is outdated." That only elevated the stakes of Obama's first meeting with Putin, which is set for Tuesday.Russia and the United States have been allies and adversaries. Obama inherited more of the latter, with relations having tanked in 2008 over Russia's war with neighboring Georgia.Obama got off to a solid start, though, with Medvedev during an April meeting in London.