As both sides sought to find some common ground Mr Tillerson said there was a "low level of trust" between the USA and Russian Federation and pledged to increase communication between Washington and Moscow.
Trump had frequently called during the 2016 United States presidential election campaign for warmer ties with Putin, despite criticism from lawmakers in his own Republican Party.
Tillerson met Putin in the Kremlin after talking to his Russian counterpart, Sergei Lavrov, for about three hours. "It can be said that the level of trust at the working level, especially at the military level, has not become better but most likely has degraded", Putin said in an interview broadcast yesterday.
US President Donald Trump has said its "certainly possible" though "probably unlikely" Russian Federation knew about the Syrian chemical attack in advance, adding relations between the US and Russian Federation were tenuous.More news: In wake of tense Trump call, Pence aims to soothe Australia
Tillerson reiterated the U.S. position that Assad must eventually relinquish power in Syria.
The US ambassador, however, added that a US commitment to the peace process was "not enough" and that Washington needed "partners who are serious about using their influence" over Syrian President Bashar al-Assad.
"We see that after Trump entered office, Washington's role in the Astana and Geneva processes was minimized", he said.
The comments come as Russian Federation vetoed a motion in the United Nations to condemn a poison gas attack believed to be launched by Bashar al-Assad's forces that killed 87 people last week.More news: McDonald's applauds crew members who recognized man wanted in Facebook video killing
Lavrov has said that US Secretary of State Rex Tillerson and he agreed at their recent meeting that new missile attacks on Syria would be unacceptable. "I think, new attempts will be made".
"It would be a fantastic thing if we got along with Putin and if we got along with Russia", Mr Trump said. "We are 100% sure that if our colleagues at the United Nations, as well as The Hague, try to avoid this investigation, this will signify that they are reluctant to find out the truth, but we will insist that the truth will be found". "No one anyone in the world should have to face that kind of suffering", she said. In a heated debate before the vote, Nikki Haley, the United States ambassador to the UN, said Russian Federation would find itself "isolated" if it failed to take action. "We're going to see how that works out".
The deal was suspended after USA missile strikes against the al-Shayrat airbase following a suspected gas attack in Khan Sheikoun, in an act Moscow labelled "aggression against a sovereign state". The Federal Bureau of Investigation is investigating whether any Trump campaign figures colluded with Moscow, which the White House denies.
"It would be wonderful... if North Atlantic Treaty Organisation and our country could get along with Russia", Mr Trump said. As a presidential candidate past year, Trump criticized Obama and Hillary Clinton, the former U.S. secretary of state during Obama's first term and Trump's opponent in the election, for getting involved in foreign conflicts and waging wars in other countries.More news: FA Cup will not impact Wenger's future at Arsenal