Putin said US-Russia trust levels have deteriorated under Donald Trump
Asked about relations since Mr Trump became president, Mr Putin said: "One could say that the level of trust on a working level, especially on the military level, has not improved, but rather has deteriorated."
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.
Moments earlier, Russian Foreign Minister Sergei Lavrov greeted Rex Tillerson with unusually icy remarks, denouncing the missile strike on Syria as illegal and accusing Washington of behaving unpredictably.
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.
Sergei Lavrov and US Secretary of State Rex Tillerson meet in Moscow
"And of course, that's not to mention that apart from the statements, we observed very recently the extremely worrying actions, when an illegal attack against Syria was undertaken."
Mr Lavrov also noted that many key State Department posts remain vacant since the new administration took office – a point of sensitivity in Washington.
Putin said the Syrian chemical attack could have been faked by Assad's enemies
One of Mr Lavrov's deputies was even more undiplomatic.
Deputy 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.
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"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."
Countries that support and oppose the missile strikes in Syria
Mon, April 10, 2017
European countries have been broadly supportive so far as President Trump ordered missile strikes against a Syrian airfield from which a deadly chemical weapons attack was launched
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SYRIA OPPOSES: President Bashar al-Assad's office denounced the U.S. strike as 'reckless, irresponsible behavior.'
He told Mr Lavrov: "I look forward to a very open, candid, frank exchange so that we can better define the U.S.-Russian relationship from this point forward."
After journalists were ushered out of the room, Mr Lavrov's spokeswoman, Maria Zakharova, wrote on her Facebook page that US journalists travelling with Mr Tillerson had behaved as if they were in a "bazaar" by shouting questions to Mr Lavrov.
Kremlin spokesman Dmitry Peskov said Mr Tillerson might meet Mr Putin later on Wednesday if the two top diplomats decided it would be useful to brief the Russian president on their talks.
Smoke rises in Daraa, Syria after airstrikes by the Syria military
But Mr Peskov too did not hold back his criticism, saying calls from Western powers for Russia to cut support for Assad amounted to giving terrorists a free hand.
Moscow's hostility to Trump administration figures is a sharp change from last year, when Putin hailed Trump as a strong figure and Russian state television was consistently full of effusive praise for him.