"We have seen very alarming actions recently with an unlawful attack against Syria", Mr Lavrov said, referring to the Tomahawk missiles Mr Trump launched at a Syrian air base to punish Assad for using chemical weapons.
"We believe it is fundamentally important not to let these actions happen again".
"The world's two foremost nuclear powers can not have this kind of relationship", Tillerson said.
He said the two sides would also discuss disagreements on Syria and how to end the country's six-year civil war.
More than 80 people were killed in what the USA has described as a nerve gas attack that Syrian President Bashar Assad's forces undoubtedly carried out. Turkey has said tests showed sarin gas was used.
Russian Federation is also denying any involvement in U.S. election hacking. He said he doesn't have have chemical weapons anymore, and that if he did, he wouldn't use them.
"There is a low level of trust between our countries", Tillerson told reporters at a joint news conference with his Russian counterpart, Foreign Minister Sergey Lavrov, after the first face-to-face meetings between Russian leaders and a top emissary of the Trump administration.
Russian Federation said the US strike was illegal though and Lavrov repeated Moscow's stance on Wednesday, saying an global investigation should be left to determine who was to blame and what happened.
"If they [Syria] use chemical weapons, they are going to pay a very, very stiff price", he said.
Meanwhile, President Trump told the Fox Business Channel that Assad was a war criminal and Russian Federation should rethink its support of him.
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And - even as Tillerson, Putin and Lavrov discussed their differences in Moscow - a fresh storm broke at the United Nations Security Council in NY.
However, the United States blames Syrian President Bashar al-Assad. The U.S. and its allies are trying to increase pressure on Russian Federation to end its support for Assad, which has been crucial in keeping the regime in power after six years of civil war. Intelligence services from several Western countries dispute that claim.
Russian Federation presented a separate draft text condemning the USA military strikes in Syria and requesting an OPCW investigation, but it was uncleaer whether that measure would come up for a vote.
"It wasn't just us - it's the entire worldwide community holding the Assad regime and its sponsors responsible for the chemical attack and indiscriminate mass murders". Conflicts over Russia's actions in Ukraine and Russia's alleged interference in the US presidential campaign were also likely topics.
But Russia made clear it had no intention to acquiesce.
Trump says Syrian President Bashar Assad is "an animal". Tillerson said he hoped for an "open and frank" dialogue with Lavrov. However, Putin appears to have found time to meet with the former recipient of Russia's Order of Friendship, who reportedly ditched his press pool to catch up with Putin.
He called the U.S. military action "genius", and stated that Xi, too, "was OK with it".
"As to the question of the interference in the election, that is fairly well established in the United States", Mr Tillerson said.
"It's not easy to get clarifications on the current as well as prospective issues because of that", Lavrov said.