Trump hopes US, Russia can get along amid tensions

US President Donald Trump offered an olive branch to Vladimir Putin on Wednesday, even as Washington and Moscow clashed over Russia's alleged US election interference and Syria's brutal conflict.

"It would be wonderful... if NATO and our country could get along with Russia," Trump said amid a deepening war of words with the Kremlin.

"Right now, we're not getting along with Russia at all. We may be at an all-time low in terms of relationship with Russia."

Trump's comments come as his administration had slammed Russia's support for Syrian leader President Bashar al-Assad and questioned the Kremlin's interference in elections in Montenegro.

Russia on Wednesday vetoed a US-backed resolution at the UN demanding the Syrian government cooperate with an investigation of a suspected chemical attack.

Trump said it was "certainly possible" that Putin knew about the attack - blamed on Assad - indicating Russian officials were present at the source airbase, which Trump later bombed.

"I would like to think that they didn't know, but certainly they could have. They were there. So we'll find out," he said.

Before Trump faced the media, Secretary of State Rex Tillerson held talks at the Kremlin that failed to bridge a deep gap of trust between the rival nuclear powers.

After the talks, Tillerson warned "there is a low level of trust between our two countries. The world's two foremost nuclear powers cannot have this kind of relationship."

The White House wants to see Russia drop its support for Assad, whom Trump labelled a "butcher."