US President Donald Trump has admitted his country's relationship with Russia "may be at an all-time low".

The top diplomats from the two countries have also acknowledged that there is little trust between them.

Moments after the US Secretary of State and Russia's Foreign Minister ended a news conference in Moscow, Russia vetoed the latest UN resolution condemning the reported use of chemical weapons in Syria.

Russian President Vladimir Putin, meanwhile, said the "level of trust" had "not improved but has rather deteriorated" under the new US administration.

During a hostile visit to Moscow, US Secretary of State Rex Tillerson also said US-Russia ties had reached a "low point" - despite a lengthy meeting with Mr Putin and Russian foreign minister Sergei Lavrov.

"The world's two foremost nuclear powers cannot have this type of relationship," Mr Tillerson warned.

He restated America's claim that Syrian government forces "planned, directed and executed" a chemical attack on civilians which killed more than 80 people.

Mr Tillerson also said that the Trump administration's position was clear: Bashar al Assad has to relinquish the presidency.

"Russia, as their closest ally in the conflict, perhaps has the best means of helping Assad recognise this reality," he told a news conference.

Both Syria and Russia have denied that forces loyal to the Assad regime carried out the toxic gas attack in the town of Khan Sheikhoun on 4 April. Moscow has blamed Syrian rebels.

Mr Lavrov denounced America's missile strikes on a Syrian airbase, launched in the aftermath of the attack, as illegal -and accused Washington of behaving unpredictably.

One of his deputies went further, telling Russia's state-owned news agency: "In general, primitiveness and loutishness are very characteristic of the current rhetoric coming out of Washington."

Relations 'are not the most calm'

Russian Foreign Minister Sergey Lavrov, left, and US Secretary of State Rex Tillerson attend a news conference following their talks in Moscow, Russia. | Image: Ivan Sekretarev/AP/Press Association Images

Mr Trump's pre-election calls for closer ties with Russia and Mr Putin seem to have been undermined by their differences over the war in Syria.

Mr Lavrov admitted relations between the two nations "are not the most calm" and some issues were "time bombs" inherited from the Obama administration.

But he said Moscow and Washington had agreed to continue co-operating to try to find a political solution for Syria.

The Russian diplomat claimed some progress was made on the crisis in the war-ravaged country and a working group would be set up to examine the poor state of US-Russia relations.

Meanwhile, Mr Trump has also declared NATO is "no longer obsolete" - and has said he is committed to the military alliance.

Before taking office in January, Mr Trump questioned the relevance of the organisation, which was created after World War Two.

He had said it was "obsolete because it was designed many, many years ago".

But in an apparent reversal, Mr Trump said the alliance is a "bulwark of international peace and security".

He again called on alliance members to spend 2% of their GDP on defence within a decade, saying they "must pay what they owe".

So far, only five of the 28 NATO members spend 2% of their GDP on defence, but the number is expected to rise next year.