"I ask the specialised (International Affairs) committee to prioritise the work on a special statement on the (Syrian) problem taking into account the recent, hopefully positive, developments," Xinhua quoted Naryshkin as saying in the opening session of the Duma.
He noted these "positive developments" were due to the "principal and consistent" position of Russia, which has recently proposed placing Syrian chemical weapons under international control.
On Monday, US Secretary of State John Kerry said Washington might reconsider its decision to strike Syria if President Bashar al-Assad turns over "every single bit" of his chemical weapons to the international community in the next week, and allows the full and total accounting of it.
Soon, Russian Foreign Minister Sergei Lavrov proposed that Damascus joins the Organisation for the Prohibition of Chemical Weapons (OPCW) and puts its chemical weapons storage facilities under international control.
Syrian Foreign Minister Walid al-Moualem was quick to welcome the proposal.
The US had previously threatened that the use of chemical weapons would be crossing a "red line".
According to Naryshkin, the US authorities knew in advance that chemical weapons would be used in Syria.
"I have a strong feeling that they (the US) knew about it for sure that the chemical weapons in Syria would be certainly used," he said.
Damascus denied that the government was behind the attack, while Moscow repeatedly called for a thorough investigation.
The Duma speaker added that Russian MPs would closely cooperate with their colleagues from countries that respect international laws.