Tillerson said Syria's government had committed more than 50 attacks using chlorine or other chemical weapons over the duration of the conflict.
Lavrov said Assad's opponents had "in essence" given guarantees for the Organisation for the Prohibition of Chemical Weapons to visit the location where at least 87 people died, but the watchdog was refusing to go.
But that one would have condemned the USA missile strikes ordered by President Donald Trump in response to the chemical attack.
The news comes after Tillerson faced an unusually chilly reception in Moscow.
Russian Federation blocked a Western-led effort at the UN Security Council on Wednesday to condemn last week's deadly gas attack in Syria and push Moscow's ally President Bashar al-Assad to cooperate with global inquiries into the incident.
Laying bare deep and risky divisions on Syria and other issues, President Donald Trump declared that USA relations with Russian Federation "may be at an all-time low".
Putin also asserted that Syria has complied with an agreement to dispose of chemical weapons "so far as we know".
Mr Tillerson opened the tense three-hour meeting with Mr Lavrov by saying he aims to clear up the two nations' "sharp differences".
Boy, 5, dies after getting head stuck at rotating restaurant
Police said a 5-year-old got his head stuck in the rotator at the restaurant Friday afternoon, ABC affiliate WSOC reported . As soon as the boy got stuck, the restaurant's employees jumped into action and tried to save him, WBTV reports.
Relations between the United States and Russian Federation have hit a low point and should be improved, Secretary of State Rex Tillerson said during a trip to Moscow Wednesday. Tillerson also told Lavrov that better relations with the USA require Russian Federation stop its support for Assad.
Donald Trump has declared that U.S. relations with Russian Federation "may be at an all-time low" laying bare deep and risky divisions on Syria and other issues, while his Secretary of State Rex Tillerson offered a similarly grim assessment after meeting with Vladimir Putin in Moscow.
Still, Tillerson sought to stress the positives from his meetings. Perhaps eager to take a shot at the previous USA administration, with whom Putin's government clashed badly, Lavrov said the new group would address "irritants which have dogged our relations over the last couple of years, particularly under the administration of President Obama".
Lavrov is also subtly mocking Tillerson for the fact that top U.S. State Department positions are unfilled. "No", Trump said in the interview, which aired Wednesday in the U.S. "Putin is backing a person that's truly an evil person". Trump says it's also "very bad for mankind".
The US and its allies say the Syrian military carried out the attack, something Syria has already denied.
Russian Foreign Minister Sergey Lavrov blasted U.S. claims that it has "irrefutable evidence" of election interference. It's unclear whether Putin will grant Tillerson a meeting.
Donald Trump (left) and Vladimir Putin.