Relations between the United States and Russia are at a low point and marked by serious distrust, US Secretary of State Rex Tillerson said after meetings in Moscow that highlighted the two countries' differences over the Syria conflict.

"There is a low level of trust between our two countries," Tillerson said on Wednesday during a news conference with Sergey Lavrov, Russia's foreign minister, adding that the "degradation" of US-Russian ties needs to end.

"The world's two foremost nuclear powers cannot have this kind of relationship," said the top US diplomat, who also met Russian President Vladimir Putin.

US and Russia have traded caustic accusations following a US strike on a Syrian airbase in retaliation for a suspected chemical attack on a rebel-held town in Syria, blamed by Washington on Syrian President Bashar al-Assad, who is backed by Russia.

Tillerson's comments echoed televised remarks by Putin, who earlier on Wednesday said the trust between the two countries had "deteriorated" since Donald Trump was elected US president.

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"One could say that the level of trust on a working level, especially on the military level, has not improved but has rather deteriorated," Putin said in an interview broadcast on Russian television.

"On Syria, they are miles apart and it doesn't seem that there's been any breakthrough at all," said Al Jazeera’s James Bays, reporting from the White House.

Airspace deal

Speaking to reporters, Tillerson reiterated Washington's position that Assad must eventually relinquish power - a position starkly at odds with Russia, which has been bombing rebel-held areas in Syria in support of Assad's forces since September 2015.

For his part, Lavrov warned against an international effort to remove Assad, citing the cases of Iraq and Libya to argue that toppling autocratic rulers by external forces leads to chaos.

He said Moscow was ready to resume a deal with Washington to avoid incidents in Syrian airspace as the two countries lead separate bombing campaigns.

"Today the president confirmed our readiness to return to its implementation on the understanding that the original aims of the air forces of the American coalition are reaffirmed, namely the fight with IS [ISIL] and al-Nusra," Lavrov said.

The deal was suspended after US missile strikes against the al-Shayrat airbase following a suspected gas attack in Khan Sheikhoun, in an act Moscow labelled "aggression against a sovereign state".

Tillerson said the US was confident in its assessment that Syrian government forces used chemical weapons in the bombing on Khan Sheikhoun and alleged that Syria had used such weapons more than 50 times in the past.

Lavrov said Russia has no intention to "shield anyone", adding that a United Nations chemical weapons watchdog must conduct an "objective and unbiased probe" into the attack that killed dozens of people.

Russian veto

Al Jazeera's Rory Challands, reporting from Moscow, said that the press conference highlighted the two diplomats' "differences in style, in position and in views of the world.

"There were no dramatic proposals made, no big deals discussed," Challands said.

"The conversation was basically about how to stop it [the relation] from getting worse, not necessarily about grand steps to make it any better."

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The press conference came just moments before Russia again cast a veto at the UN Security Council, blocking a bid from the US, UK and France to condemn the suspected gas attack and push the Syrian government to cooperate with investigators.

China, which has vetoed six resolutions on Syria since the civil war began six years ago, abstained from Wednesday's vote, along with Ethiopia and Kazakhstan.

Ten countries voted in favour of the text, while Bolivia joined Russia in voting no.