Asked about accusations that Syria's government launched a chemical weapons attack in Idlib province, Mr Putin said that Damascus had given up its chemical weapons stocks.
He said he believed there were two main explanations for the incident in Idlib province: that Syrian government air strikes had hit rebel chemical weapons stocks, releasing poisonous gas, or that the incident was a set-up designed to discredit the Syrian government.
The comments were made in an interview transcript released by the Kremlin.
Mr Putin doubled down on Russia's support for Syrian President Bashar al-Assad, repeating denials that Assad's government was to blame for the gas attack last week and adding a new theory that the attack may have been faked by Assad's enemies.
He said: "I won't hide the fact that we have a lot of questions, taking into account the extremely ambiguous and sometimes contradictory ideas which have been expressed in Washington across the whole spectrum of bilateral and multilateral affairs.
EPAMr Lavrov also noted that many key State Department posts remain vacant since the new administration took office - a point of sensitivity in Washington.
EPADeputy Foreign Minister Sergei Ryabkov said: "In general, primitiveness and loutishness are very characteristic of the current rhetoric coming out of Washington. We'll hope that this doesn't become the substance of American policy.
"As a whole, the administration's stance with regards to Syria remains a mystery. Inconsistency is what comes to mind first of all."
Mr Tillerson kept to more calibrated remarks, saying his aim was "to further clarify areas of sharp difference so that we can better understand why these differences exist and what the prospects for narrowing those differences may be."