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The US secretary of state has warned Russia's foreign minister of "serious mistrust" between the two nations due to Moscow's US election interference.

Rex Tillerson said Russia's actions had damaged the relationship, but added it's not "useful to just cut everything off over one single issue".

The US will respond by 1 September to Russia's expulsion of 755 staff from the US embassy in Moscow, he said.

US intelligence agencies believe the Kremlin tried to help Donald Trump.

Moscow vehemently denies any efforts to influence the US election, and retaliatory sanctions passed by Congress last month - against President Trump's wishes - have sparked a tit-for-tat.

Mr Tillerson told Russian Foreign Minister Sergei Lavrov there was now "serious mistrust between our two countries and that we simply have to find some way to deal with that".

After speaking to Mr Lavrov on the sidelines of the ASEAN meeting in the Philippines, he said: "We have our differences, we're going to have to continue to find a way to address those."

He said he met Mr Lavrov to "help them understand how serious this incident had been and how seriously it damaged the relationship."

Mr Tillerson also indicated that the two countries may be able to come together to begin discussions on violence in Eastern Ukraine.

The comments by the former CEO of Exxon Mobil come less than a week after US President Donald Trump signed into law the new legislation that imposes sanctions on Russia for both election meddling and military actions in Crimea and Ukraine.

The law also prevents Mr Trump from lifting sanctions or returning Russian diplomatic compounds in the US that were seized by the Obama administration in retaliation for the alleged meddling.

The president has failed to singularly point the finger at Moscow for the hacking of Democratic Party emails during the final stages of the election campaign.

And he has condemned the investigations, which are also looking at whether his campaign team colluded with Moscow, as a witch hunt.

After signing the bill, Mr Trump decried it, arguing that it limited his ability to negotiate with Russia.