The United States has cautiously raised concern over Russia's alleged interference in last year's presidential election and its effect on relations between the two nations.

US Secretary of State Rex Tillerson said on Monday that he had told Russian Foreign Minister Sergey Lavrov that Moscow's meddling in the vote created "serious mistrust" between the two countries.

"Russian meddling in the elections was certainly a serious incident," Tillerson told reporters after meeting Lavrov on Sunday on the sidelines of the ASEAN summit in the Philippine capital, Manila. "We talked about that in the discussion that we had with Mr Lavrov yesterday."

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Tillerson said he had tried to help Lavrov understand "just how serious this incident had been".

"This had created serious mistrust and ... we simply have to find some way to deal with that," he said.

Tillerson added that it was pointless to cut ties over disagreements between the two countries, adding that Lavrov had indicated some "willingness" to talk and find ways to move forward on the issue of Ukraine.

US Congress and a special prosecutor are investigating allegations that Russians managed to tip the results of the historic vote last year in US President Donald Trump's favour.

Russia has furiously denied the claims, which have been endorsed by US intelligence agencies.

'Full-scale trade war'

Trump has also played down the allegations, but the ongoing controversy has strained already tense ties.

Congress overwhelmingly approved new sanctions against Russia, which Trump grudgingly signed last week, for its role in the 2016 vote and the annexation of Ukraine's Crimea.

Russian Prime Minister Dmitry Medvedev said the new US sanctions against his country amount to a "full-scale trade war".

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In retaliation, President Vladimir Putin ordered the US diplomatic mission in Moscow to cut 755 personnel.

Tillerson said he had also warned Lavrov that Washington was deciding on a response to the Kremlin's move.

"I told the foreign minister that we have not made a decision about how we would respond to the Russian request to remove US diplomatic personnel," Tillerson said.

"I asked several clarifying questions, just to describe the thinking behind that diplomatic note that we received, but I told them we would respond by September 1," he said, referring to Moscow's deadline to shrink the mission.