Of Assad, Trump added: "This is an animal".
He said there was a "low level of trust" and "the world's two foremost nuclear powers can not have this kind of relationship".
Tillerson said much of the same following a joint press conference with Lavrov, attributing the two countries' problems to a lack of trust, but wouldn't go as far as Trump when it came to speculating about Russian awareness of the chemical attack.
US Central Command said that coalition aircraft were given the wrong coordinates by their partner forces, the predominantly-Kurdish Syrian Democratic Forces, for a strike meant to target Islamic State militants south of their Tabqa stronghold.
"The world's two foremost nuclear powers can not have this type of relationship", Mr Tillerson warned.
The proposed resolution would have condemned the alleged attack and expressed the council's full backing to investigators from the Organization for the Prohibition of Chemical Weapons (OPCW).
Tax deadline: Is Trump paying his fair share?
Protesters are taking to the streets across the country to demand that President Donald Trump release his tax returns. Liberals and anti-Trump conservatives alike joined the roughly 100 protests held across the country . "We do care.
"A successful ouster of a dictator is for me very hard to remember", Lavrov said. Assad referred to the aftermath of the attack seen on social media and in the news as a "play".
Syria denied any use of chemical weapons and Russian Federation backed its claim.
Despite hopes of an improvement in ties under Trump, the Tillerson-Lavrov talks look set to be dominated by the war of words over Syria - where more than 320,000 people have died in six years of brutal war.
The two did outline some areas of agreement Wednesday.
He said such visual evidence doesn't make it "clear whether it happened or not". -Russian relations may be at an all-time low. Still, the question of removing Assad from power remained a sticking point. The secretary did reiterate the position that he and others have taken in the days since last week's chemical weapons attack, that "the reign of the Assad family is coming to an end".
Bilic says Irons must be… West Ham united
Despite all the public backing from his board via the media, Slaven Bilic's position at West Ham now isn't the most comfortable. The lead was doubled in the 68th minute as Ozil turned provider to pick out Walcott, who side-footed home from 12-yards out.
Rex Tillerson, secretary of state: We had a lengthy discussion on the situation in Syria and shared perspectives on possible ways forward.
The US and its allies say the Syrian military carried out the attack, something Syria has already denied.
He added: "Putin is the leader of Russian Federation". Lavrov, however, pointed to the downside of removing a foreign leader.
He said the visit - the first to Moscow by a senior Trump administration official - offered an opportunity to clarify the chances of cooperation "above all on the formation of a broad anti-terrorist front". "I do not know who saw them".
NCAA adopts early signing period, 10th coach for football
In a vote Friday, the NCAA's Division I Council gave the go-ahead for an early signing date in college football. FBS schools are allowed to hire a 10th assistant coach (beginning in January 2018).