Russia has criticised US President Barack Obama's State of the Union address, claiming that it revealed the US seeks world domination.

Obama used the annual speech to reject Russia's foreign policy in Ukraine, where the West has accused Moscow of fomenting a civil war and supplying weapons and fighters to pro-Russian separatists.

In its efforts to support democracy in Ukraine, Obama said, the US had upheld "the principle that bigger nations can't bully the small".

Russia's top foreign policy official rejected the narrative and said the US was seeking to be "number one" in the world.

"The Americans have taken the course of confrontation and do not assess their own steps critically at all," said Russian Foreign Minister Sergei Lavrov.

Obama's State of the Union address "shows that at the centre of the philosophy is only one thing: 'We are number one and everyone else has to respect that.'... It shows that the US wants all the same to dominate the world and cannot merely be the first among equals," Lavrov told a news conference in Moscow.

US-Russia relations have slumped to their lowest point since the end of the Cold War, amid rising tensions over the Syrian civil war and competing foreign policy goals in Ukraine.

The US has backed the pro-European non-violent movements in Ukraine, causing alarm in Moscow amid fears that the US was seeking to expand the reach of Nato in eastern Europe.

Russia annexed the Ukrainian peninsula of Crimea in March 2014, and has been accused of launching and fuelling the conflict in eastern Ukraine in April.

Fighting in eastern Ukraine has intensified in recent weeks, despite an official ceasefire in the region.

The United Nations has estimated that 4,800 people have been killed in the fighting since then.