The Kremlin on Friday slammed Joe Biden's "very aggressive rhetoric" after the new US president said Washington's relationship with Moscow would change and demanded opposition politician Alexei Navalny's release. 

"We've already said that we will not heed patronising statements of this sort. We will not do it," Kremlin spokesman Dmitry Peskov told reporters. 

"This is very aggressive and unconstructive rhetoric."

President Vladimir Putin's spokesman acknowledged a "huge amount of differences and different approaches to key issues" but he also indicated that Moscow wanted to continue cooperation with Washington under Biden.

"We expect to see Americans' political will to continue cooperation where this serves our interests," he said.

In toughly worded remarks pivoting from his predecessor Donald Trump's muted approach to Moscow, Biden on Thursday warned of "advancing authoritarianism" in China and Russia.

He said the United States would no longer be "rolling over in the face of Russia's aggressive actions" and demanded the release of Putin's jailed critic Navalny who this week was sentenced to nearly three years in prison on old embezzlement charges.

Biden said there were areas where he was willing to work with the Kremlin, notably the New START treaty on curbing nuclear weapons, which the two countries extended for five years this week.