The US secretary of state says there is a "low level of trust" between Washington and Moscow and they "cannot have this kind of relationship".
Rex Tillerson gave his frank assessment at a news conference following two hours of talks with Russian President Vladimir Putin at the Kremlin.
Mr Tillerson, who has also had talks with Russian foreign minister Sergei Lavrov, admitted that US-Russian ties were at a "low point" amid Moscow's continued support for President Bashar al Assad's regime in Syria.
He said there was a "low level of trust" and "the world's two foremost nuclear powers cannot have this kind of relationship".
He also reiterated America's claim that Syrian government forces "planned, directed and executed" a chemical attack on civilians which killed more than 80 people.
Mr Tillerson repeated the US administration's belief that "the reign of the Assad family is coming to an end".
But sitting alongside the secretary of state at the lengthy news call, Mr Lavrov warned against an international effort to oust Mr Assad from power, saying his removal would help Islamic State.
As expected, on Wednesday evening Russia vetoed a UN resolution put forward by France, the UK and US condemning the attack and calling for the Assad government to cooperate with investigators.
Syria and Russia have both denied that Assad's forces carried out the toxic gas attack in the town of Khan Sheikhoun last week. Moscow has blamed Syrian rebels.
UK analysis of samples from the scene has detected sarin or a sarin-like substance .
Following the 4 April atrocity, President Donald Trump ordered a cruise missile strike on a Syrian regime airbase from where the chemical attack was allegedly launched. The move angered Russia.
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 cooperating 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.
The pair also found time to discuss other crises including US tensions with North Korea and the Ukraine conflict.
The Putin-Tillerson meeting was believed to be the first between the Russian President and a top member of Mr Trump's administration since the US businessman took office in January.
It is not the first time Mr Putin and Mr Tillerson have had talks.
The Russian leader has previously met the American when he was head of US oil giant ExxonMobil.