A 29-year-old Russian woman has been arrested for conspiring to influence US politics by cultivating ties with political groups including the National Rifle Association, the powerful gun rights lobby.

Mariia Butina, whose name is sometimes spelled Maria, was arrested in Washington on Sunday and appeared in court on Monday, the Justice Department said.

Butina was charged with conspiring to act as an agent of Russia "by developing relationships with US persons and infiltrating organizations having influence in American politics," it said in a statement.

Her arrest was announced as President Donald Trump flew back from Helsinki to Washington, following an inaugural summit with Vladimir Putin at which he was accused of failing to stand up to the Russian leader over electoral meddling.

The Justice Department said Butina had broken US law by not disclosing to US authorities that she was acting on behalf of the Russian government.

Butina had close ties to a "Russian official" who was not identified in the charging documents but who has been widely reported to be a Russian politician named Alexander Torshin, it said.

An ally of Russian leader Putin, Torshin is currently a senior official with Russia's central bank and a former top Russian lawmaker. He is one of a number of senior Russian officials subject to US sanctions.

The Justice Department said Butina carried out her activities in the United States at the direction of the "Russian official."

It said Butina and the official sought to develop relationships with US politicians to create "back channel" lines of communications that could be "used by the Russian Federation to penetrate the US national decision-making apparatus."

The announcement of Butina's arrest comes three days after 12 Russian intelligence operatives were indicted by a US grand jury for hacking Hillary Clinton's 2016 presidential campaign and the Democratic Party.