Mr Peskov said in a conference call with reporters that President Putin's meeting with Mr Tillerson reflected the "understanding of the need to maintain a dialogue to search for solutions".
Tillerson's trip to Russia, his first as secretary of state, followed just days after a US missile strike against the regime of Assad, a Russian ally.
"The current state of US-Russia relations at low point -there is a low state of trust between our two countries".
Others said the statements should clear up any doubts about U.S. -Russia relations.
Details of the meeting were not released.
But Russian Foreign Minister Sergei Lavrov, referring to Iraq, said, "Experiments like that, which are built on an obsession with overthrowing dictators, totalitarian or authoritarian leaders, we have already seen".
Russian Federation remains furious, and the us and Russian Federation have been confronting each other over it both at the United Nations and in meetings Secretary of State Rex Tillerson had with both Foreign Minister Sergey Lavrov and Putin in Russian Federation on Wednesday.
"There is a low level of trust between our two countries", Tillerson added.
"The world's two foremost nuclear powers can not have this sort of relationship".
Tillerson said President Donald Trump's administration was of the view that Syrian President Bashar al-Assad "cannot stay in power".
He said Russian Federation was "collaborating with Assad who is the biggest terrorist of all".
Trump made the remark at a joint press conference with visiting NATO Secretary General Jens Stoltenberg at the White House.
The U.S. and European nations have increased pressure on Putin to sever ties with Assad, so far to no avail.
Russian Deputy U.N. Ambassador Vladimir Safronkov shows his hand to vote against a resolution condemning Syria's use of chemical weapons, Wednesday, April 5, 2017, at U.N. headquarters.
Russia's U.N. Ambassador Vladimir Safronkov told the council before the vote that during talks in Moscow Russia asked for an independent global investigation to examine the April 4 attack on Khan Sheikhoun.
Tuesday, the White House declassified a US intelligence report that accused Putin of a cover-up to "confuse" and "obfuscate" on behalf of Assad. "But when I see people using frightful, terrible chemical weapons, which they agreed not to use under the Obama administration, but they violated it", he said, explaining the strike. "That's exactly what is happening now..."
The Trump administration had previously appeared open to working with Assad and Syria to prioritize the fight against terrorism, but President Trump said he was moved to take action by photos of children suffering and dying in the chemical attack.
"It'd be a fantastic thing if we got along with Putin and if we got along with Russia", Trump said.