By Euan McKirdy and Angela Dewan

CNN

(CNN) -- Russian Foreign Minister Sergey Lavrov began a meeting with his US counterpart Rex Tillerson in Moscow with a warning -- do not strike the Syrian regime again.

The two top diplomats are sitting down together in Moscow on Wednesday for what are expected to be painstaking talks, after a chemical attack in northwestern Syria plunged the old Cold War enemies to a new low.

The two countries have traded barbs over last week's chemical attack, which killed 89 people, and prompted the US to carry out its first strike against the Syrian regime in the six-year conflict, taking out aircraft and infrastructure at a Syrian military air base.

The White House on Tuesday accused Russia and Syria of carrying out a confusion campaign over who was responsible for the chemical attack. Russian President Vladimir Putin has made comparisons between the US response and its 2003 intervention in Iraq, calling it a "tedious" story.

The deaths have been widely blamed on Syrian President Bashar al-Assad's regime, but Russia, Assad's most powerful ally, has denied the regime carried out the attack.

Lavrov said Wednesday that Russia "saw some very troubling actions regarding the attack on Syria."

"We believe it is fundamentally important not to let these actions happen again," Lavrov said, according to an official Russian interpreter.

He also complained about the mixed messages coming out of Washington on the Trump administration's policy on Syria, with the US envoy to the UN, Nikki Haley, making clear Assad should have no future in Syria as Tillerson took a softer line.

"I will be frank that we had a lot of questions regarding a lot of very ambiguous as well as contradictory ideas on a whole plethora of bilateral and international agenda coming from Washington," Lavrov said.

He hit back at remarks Tillerson made a day earlier that Russia would have to decide whether it was with the US and the West in standing up against Assad, or against them, describing the comments as "wrong choices."

Tillerson took a more diplomatic tone in his opening remarks, saying that he hoped to clarify "areas of common objectives, areas of common interests, even when our tactical approaches may be different."

"And to further clarify areas of sharp difference, so we can better understand why these differences exist and what the prospects for narrowing those differences may be."

The fallout over the chemical attack follows comments by the Trump administration and Russia that a reset in relations between the countries was possible after decades of hostility.

But Putin said in an interview with state-run MIR television station that relations had only deteriorated.

"The working level of confidence in Russian-American relations, especially at the military level, under the administration of Donald Trump, has not improved, but rather worsened".

Russia's position

Washington has said that Russia and Syria are trying to "confuse the world community about who is responsible for using chemical weapons against the Syrian people in this and earlier attacks."

Russia claims the Syrian regime is being unfairly blamed for the chemical attack, and on Wednesday Putin said that the attack was "simply staging" and a provocation, in his interview with MIR.

Putin suggested on Monday that forces within Syria were plotting more chemical attacks, including near Damascus, that they intended to pin on the Syrian regime.

Moscow earlier claimed that the deaths had been caused when a Syrian regime airstrike hit a chemical weapons stockpile held by terrorist groups.

But Syria gave a murky account of what happened, denying its planes were in the air at the time of the dawn attack, claiming it carried out its first strike that day five hours later, hitting the alleged chemical weapons cache.

What is the US' Syria policy?

Following the chemical attack, US President Donald Trump ordered a Tomahawk missile strike against the Shayrat airfield in Syria, from where the US says the aircraft took off to launch the attack.

The US claims the strike destroyed 20% of Syria's operational aircraft, a figure disputed by Russia's Defense Ministry.

But the White House has also caused a great deal of confusion -- the US position on Syria is still woefully unclear, as Trump has made no public statement on Syria since last week's missile attack.

White House press secretary Sean Spicer has said that the Trump administration would respond if the Assad regime used barrel bombs against his own people, something that has been a regular occurrence in the six-year civil war. Aides later clarified that this "did not signal a change in administration policy."

Haley, the UN envoy, said removing Assad from power was a priority, whereas Tillerson said he merely "hoped" the Syrian people would choose to oust Assad and reiterated that defeating ISIS was the US' first priority in Syria.

US Defense Secretary James Mattis has said that while defeating ISIS was first priority, further use of chemical weapons by the Assad regime would not be tolerated and could warrant additional military action.

"If they use chemical weapons, they are going to pay a very, very stiff price," Mattis told reporters during his first Pentagon briefing as secretary.

CNN's Theodore Schleifer, Nic Robertson, Ryan Browne and Ben Westcott contributed to this report.