On Tuesday, the world body's special envoy Staffan de Mistura told reporters in Geneva he wanted "to proceed with a third round of intra-Syrian talks towards the end of August" after two previous rounds of talks this year ended in failure.
De Mistura has struggled to keep the peace process alive amid a surge in fighting between Syrian President Bashar al-Assad's forces and rebel groups.
"I informed the minister and his deputy of the intention of the special envoy De Mistura to reconvene the inter-Syrian talks towards the end of August," Ramzy said after meeting Foreign Minister Walid Muallem and his deputy Faisal Muqdad.
He said Muallem "confirmed the intention of the Syrian government to participate in these talks once they are held".
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Muqdad said Syria's government was "ready to resume the talks with no preconditions in an inter-Syrian context with no foreign interference", the official SANA news agency reported him as saying.
De Mistura's announcement comes with the armed opposition facing difficulties, especially in the northern city of Aleppo where government forces are besieging rebel-held districts.
The UN-brokered talks have so far been deadlocked over Assad's fate.
The government has ruled out negotiations on his possible departure, while the main opposition High Negotiations Committee has said it will not agree to any deal that leaves Assad in power.
Since Syria was plunged into chaos in 2011, more than 280,000 people have been killed and upwards of half the population has been displaced.