By Matt Spetalnick and Oleg Shchedrov

MOSCOW (Reuters) - U.S. President Barack Obama and Kremlin leader Dmitry Medvedev agreed outline cuts in nuclear arsenals and a deal to let U.S. troops fly across Russia, on the first day of an Obama visit intended to mend strained relations.

The two countries, which between them possess 95 percent of the world's nuclear weapons, pledged to finalize a new arms treaty cutting the number of deployed warheads to 1,500 to 1,675 from current levels above 2,200.

Russia will also allow 4,500 flights a year carrying U.S. troops and weapons to the war in Afghanistan to transit its vast territory free of charge, a move hailed by the U.S. side as showing Moscow's willingness to help in the war on the Taliban.

Other deals covered military cooperation, the creation of a new joint government commission and new investment, according to texts released by officials.

"We are confident that we can continue to build on the excellent discussions that we had in London," Obama told President Dmitry Medvedev at the start of talks in the Kremlin, referring to the first meeting the two leaders had in April.

"And that on a whole host of issues ... the United States and Russia have more in common than they have differences and that if we work hard in these next few days we can make extraordinary progress..."

But clouds remained on the horizon.

Senior Russian officials repeatedly emphasized in the run-up to the visit that Moscow will not sign a landmark deal cutting nuclear arms later this year unless Obama makes concessions on U.S. plans for an anti-missile system in Europe, a project hated by the Kremlin which fears it could threaten Russia's security.

The leaders played down those differences at the Kremlin and an agreed statement on missile threats contained only a generally worded pledge to continue to work together to evaluate threats from ballistic missiles.

Medvedev, smiling broadly as he welcomed Obama in the Green Parlour of the Kremlin, said he hoped that "as a result of our conversations ... we will close a number of difficult pages in Russian-American relations and turn a new page."

Earlier Russian Deputy Foreign Minister Sergei Ryabkov greeted Obama, his wife Michelle and their two daughters as they stepped from Air Force One at Moscow's Vnukovo airport under unseasonably cold, cloudy skies.

The arrival was not shown live on Russian television and there was generally little sign in Moscow of the "Obamamania" which has greeted the U.S. leader on some other foreign trips.

Obama's motorcade sped alone along a barricaded highway from the airport toward the Tomb of the Unknown Soldier for a wreath-laying ceremony. On the city's outskirts, small groups of onlookers smiled and waved but most looked on without reaction.

Business leaders traveling with Obama want to use the visit to boost trade and investment. Russian trade with the United States was just $36 billion in 2008, the same amount as with Poland, and investment has lagged that of European competitors.

"We hope that President Medvedev will be able to follow through on his continuous campaign to improve the rule of law," Andrew Somers, president of the American Chamber of Commerce in Russia, told Reuters in an interview.

"I think this is a single biggest inhibitor to investment by U.S. companies, their concern about the rule of law."

Obama will also listen to the country's embattled democratic opposition, meet former Soviet leader Mikhail Gorbachev and make a major speech to Russian students.

But he faces a harder task in trying to achieve his avowed aim of a "reset" in relations between Washington and Moscow.

GEORGIA WAR HURT TIES

Ties hit their worst level since the 1990s last year after Russia sent troops into neighboring Georgia, a U.S. ally, triggering fierce condemnation from Washington.

The two sides remain still deeply divided over the U.S. missile defense plans. Neither have they come to an agreement on such fundamental issues as Russia's accession to the World Trade Organization or the future of Georgia, where Moscow recognizes as independent states two rebel Georgian regions Tbilisi considers part of its territory.

A poll released on the eve of Obama's arrival showed Russian distrust of the United States. The University of Maryland survey found 75 percent of Russians believed the United States abused its greater power and only two percent had "a lot of confidence" Obama would do the right thing in world affairs.

Medvedev, in an interview released on Sunday, said the United States would only get a full arms control treaty with Moscow if it dropped unilateral plans for missile defense -- a linkage which Obama has rejected.

The U.S. leader also faces an awkward first meeting on Tuesday with Prime Minister Vladimir Putin, Russia's most powerful politician, after publicly criticizing him last week. Putin was out of Moscow on Monday visiting a combine harvest factory in southern Russia.

(Additional reporting by Jeff Mason, Guy Faulconbridge, Dmitry Sergeyev and Amie Ferris-Rotman; writing by Michael Stott; editing by Jon Boyle)