Moscow's willingness to harbor National Security Agency leaker Edward Snowden is an example of the kinds of "underlying challenges'' that keep getting in the way of his efforts to ease tensions between the former Cold War rivals, Obama says.
Some of the other issues frustrating U.S.-Russian relations:
The two nations are at odds over the civil war. Russia has shielded Syrian President Bashar Assad from international sanctions and provided him weapons, despite an international outcry.
The U.S. says Russia's support is allowing Assad to cling to power despite more than two years of violence which, according to United Nations estimates, already has killed 100,000 of his people.
Obama is seeking at least a modicum of cooperation from Russia to make way for the U.S. goal of ousting Assad. If they would, Russian leaders are in a position to persuade Assad to join rebels in peace talks to negotiate his departure.
Russians have a long-standing beef about the U.S. missile defense system planned for Europe, dating back to the Reagan administration's disputes with the Soviet Union. The Russians see the system as a threat to the viability of their own nuclear arsenal as a deterrent. American officials have always maintained that the missile defenses are meant to protect NATO allies and counter any threat from Iran.
Obama was denounced by Republican critics when in March 2012 he was caught, unaware that he was speaking into an open microphone, assuring Russia's then-president Dmitry Medvedev that he would have more flexibility on the issue once re-elected. Russia complains there's been little sign of movement on missile defense since Election Day.
Americans object to the way Russian leaders have tried to silence critical voices.
The White House said it was "deeply disappointed and concerned'' when opposition leader Alexei Navalny was sentenced to five years in prison on embezzlement charges last month. A colorful blogger turned protest leader, Navalny challenged the Kremlin by exposing corruption, mocking Russian leaders and running for mayor of Moscow.
In April, the U.S. imposed financial sanctions on 18 Russians over human rights violations. The sanctions were sparked by the death in prison of a Russian lawyer, Sergei Magnitsky, who had accused police and officials of stealing $230 million in tax rebates. Officials accused of profiting from the scheme or persecuting Magnitsky were hit with sanctions.
U.S. leaders joined musicians and free speech advocates around the globe in denouncing the imprisonment last year of members of the punk rock band Pussy Riot. The three women were convicted of hooliganism after staging an anti-Putin protest inside a Russian Orthodox Church.
Putin bristles at the U.S. criticism.
Putin signed a law last year banning U.S. adoptions of Russian children. The move was viewed within the U.S. as retaliation for the Magnitsky law that set in motion human rights sanctions against Russian officials.
After returning to the presidency last year, Putin has waged a campaign of harassment and intimidation against civil society groups, the non-governmental organizations that take up causes such as protecting human rights, helping immigrants, defending voters' rights or promoting environmental protection.
Russia also expelled the U.S. Agency for International Development, which had promoted democracy and civil societies in Russia for two decades.
The Kremlin accused USAID of using its $50 million annual budget to influence Russian politics and elections and weaken Putin's hold on power.
Violence against gays long has been a problem in Russia. Now the U.S. is criticizing Russia for an official crackdown on gay rights.
A new Russian law imposes fines and up to 15 days in prison for people accused of spreading "propaganda of nontraditional sexual relations'' to minors. The law covers views expressed online or in the news media. And it bans gay pride rallies.
Russian officials say the law will be enforced during the 2014 Olympics in the city of Sochi.
Asked about that Tuesday on "The Tonight Show,'' Obama said he has "no patience'' for countries that intimidate or harm people because of their sexual orientation.