MOSCOW (Reuters) - Russian President Vladimir Putin spoke to Barack Obama by telephone and congratulated him a second time over his victory in the U.S. presidential election, the Kremlin said on Tuesday.

Putin wished Obama success in "forming a new team" and the two leaders "confirmed their interest in the consistent development of bilateral relations in all areas including economic aspects," the Kremlin said in a statement.

Putin repeated an invitation to visit Russia and Obama expressed readiness to do so, the statement said.

Putin had sent a Obama a telegram on November 7, the day after the election, congratulating him on winning "by a big margin" after a tough campaign and saying he hoped Obama would visit Russia next year.

Relations between Moscow and Washington, badly damaged by Russia's 2008 war with pro-Western Georgia, improved after Obama moved to "reset" ties early in his first term and signed a nuclear arms treaty with then-President Dmitry Medvedev in 2010.

Ties between the nuclear-armed Cold War foes have been strained since by disputes over issues including uprisings in Libya and Syria, Putin's accusations of U.S. support for opposition protests, U.S. missile defense plans and U.S. criticism of the jailing of Russian punk band Pussy Riot.

Obama's relationship with Medvedev is seen as warmer than with Putin but the Russian leader made clear he preferred Obama to Mitt Romney, saying in September that the Republican's criticism of Russia was "mistaken" and calling Obama "an honest person who really wants to change much for the better".

In a foreign policy decree issued after his inauguration to a six-year term in May, Putin said Moscow wanted to bring cooperation with Washington "to a truly strategic level" but that the United States must treat Russia as an equal and refrain from interfering in its affairs.

(Writing by Steve Gutterman; Editing by Robin Pomeroy)