Peskov was speaking to reporters two days after Idlib’s town of Khan Shaykhun was subject to a chemical weapon attack that left at least 100 people dead and hundreds more injured, mostly children.
The attack attracted widespread international condemnation and calls for the Assad regime to be held accountable.
The Syrian regime has denied allegations it targeted the area with chemical weapons.
Peskov said the evidence produced so far was not credible.
He also said Russia believed the use of chemical weapons was unacceptable.
Last year, a UN-appointed investigation panel found that chemical weapons were mainly used by Syrian regime forces in 2014 and 2015. No punitive measures were taken, however.