Updated April 13, 2017 12:10:11

President Donald Trump says US-Russian relations "may be at an all-time low", echoing the sentiment of Secretary of State Rex Tillerson.

The comments came after Mr Tillerson was greeted with a frosty reception when he met with Russian Foreign Minister Sergei Lavrov and later with President Vladimir Putin in Moscow.

Only weeks ago it appeared Mr Trump — who praised Mr Putin throughout the US election campaign — was poised for a potentially harmonious relationship with Russia unlike many of his predecessors.

But any such expectations have crashed into reality amid the nasty back-and-forth over Syria in the wake of the US launching 59 missiles on the country.

"It would be wonderful … if NATO and our country could get along with Russia," Mr Trump said during a White House news conference.

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

Mr Trump, who last week ordered the airstrikes in retaliation for a chemical weapons attack that left more than 70 dead, was asked if Syria could have launched the attack without Russia's knowledge.

"I would like to think that they [Russia] didn't know, but certainly they could have, they were there," he said.

"We'll find out. General [James] Mattis is looking into it with the entire Pentagon group that does that kind of work."

Mistrust between nuclear powers untenable, Tillerson says

In his talks, dominated by the war in Syria, Mr Tillerson reiterated the US position that Syrian President Bashar al-Assad must eventually relinquish power in Syria, a position starkly at odds with Russia.

For years we have been aware of evidence that Bashar al-Assad may not have declared all of his chemical weapons stockpiles — and these strikes highlight the dilemma about what to do now, writes Matt Brown.

"There is a low level of trust between our two countries," Mr Tillerson said.

"The world's two foremost nuclear powers cannot have this kind of relationship."

But Mr Lavrov warned Mr Assad's removal was not a good idea and would only serve to benefit the Islamic State group in the long run.

"I don't remember any positive examples of how a dictator was overthrown and everything was just fine afterwards," Mr Lavrov said.

"It's in our interests not to allow the Islamic State ... to hold court in Damascus," he said.

Meanwhile back in the US, Russia again blocked a Western effort at the United Nations Security Council to condemn last week's deadly gas attack in Syria and pressure Mr Assad to cooperate with international inquiries into the incident.

It was the eighth time during Syria's six-year-old civil war Moscow has used its veto power on the Security Council to shield Mr Assad's Government.

US Ambassador to the United Nations, Nikki Haley, warned Moscow against protecting Mr Assad, who relies on support from Russia and Iran in his conflict with mostly Sunni Muslim rebels.

"To my colleagues from Russia — you are isolating yourselves from the international community every time one of Assad's planes drop another barrel bomb on civilians and every time Assad tries to starve another community to death," Ms Haley said.

Mr Tillerson met with Mr Putin in the Kremlin after talking to Mr Lavrov for about three hours. The Kremlin had previously declined to confirm Mr Putin would meet Mr Tillerson, reflecting increasing tensions.

The meeting was the first between Mr Putin and a top member of Mr Trump's administration since the new American President took office in January.

Tillerson's icy reception in Moscow

As Mr Tillerson arrived in Moscow he was given an unusually hostile reception as the two countries prepared to face-off over Syria.

Just as Mr Tillerson sat down for talks, a senior Russian official assailed the "primitiveness and loutishness" of US rhetoric, part of a volley of statements that appeared timed to maximise the awkwardness during the first visit by a member of Mr Trump's cabinet.

"One could say that the level of trust on a working level, especially on the military level, has not improved but has rather deteriorated," Mr Putin said on Russian television before meeting Mr Tillerson.

Moments earlier, Mr Lavrov greeted Mr Tillerson with icy remarks, denouncing the missile strike on Syria as illegal and accusing Washington of behaving unpredictably.

"I won't hide the fact that we have a lot of questions, taking into account the extremely ambiguous and sometimes contradictory ideas which have been expressed in Washington across the whole spectrum of bilateral and multilateral affairs," Mr Lavrov said.

"And of course, that's not to mention that apart from the statements, we observed very recently the extremely worrying actions, when an illegal attack against Syria was undertaken."

Mr Lavrov also noted that many key State Department posts remained vacant since the new administration took office — a point of sensitivity in Washington.

One of Mr Lavrov's deputies, Deputy Foreign Minister Sergei Ryabkov was even more undiplomatic talking to Russia's state-owned RIA news agency.

"In general, primitiveness and loutishness are very characteristic of the current rhetoric coming out of Washington. We'll hope that this doesn't become the substance of American policy," he said.

"As a whole, the administration's stance with regards to Syria remains a mystery. Inconsistency is what comes to mind first of all."

Moscow's hostility to Trump administration figures is a sharp change from last year, when Mr Putin hailed Mr Trump as a strong figure and Russian state television was consistently full of effusive praise for him.

Photo: A satellite image shows the damage following a US airstrike on the Shayrat military airbase in Syria. (AP: DigitalGlobe)

Moscow accused of cover-up

The White House has accused Moscow of trying to cover up Mr Assad's use of chemical weapons after the attack on a town killed 87 people last week.

Mr Trump responded to the gas attack by firing 59 cruise missiles at a Syrian air base on Friday. Washington warned Moscow, and Russian troops at the base were not hit.

The missile attack came after years of heated debate and deliberation in Washington over intervention in Syria's bloody civil war.

Moscow has stood by Mr Assad, saying the poison gas belonged to rebels, an explanation Washington dismisses as beyond credible.

Mr Putin said that either gas belonging to the rebels was released when it was hit by a Syrian strike on a rebel arms dump, or the rebels faked the incident to discredit Mr Assad.

Mr Trump came to the presidency promising to seek closer ties with Russia and greater cooperation fighting against their common enemy in Syria, the Islamic State group.

Mr Tillerson is a former oil executive who was awarded Russia's Order of Friendship by Mr Putin.

Last week's poison gas attack and the US retaliation upended what many in Moscow hoped would be a transformation in relations between the two countries, which reached a post-Cold War low under Mr Trump's predecessor Barack Obama.

ABC/Wires

Topics: foreign-affairs, government-and-politics, world-politics, unrest-conflict-and-war, russian-federation, united-states, syrian-arab-republic

First posted April 13, 2017 01:00:14