The Secretary of the Security Council Umerov reported that he had proposed a further meeting with the Russian side next week. The impetus for negotiations needs to be boosted, said Ukrainian President Volodymyr Zelensky.
Mr Zelensky reaffirmed his readiness to meet directly with Russian President Vladimir Putin.
A meeting at the leadership level is necessary to truly ensure long-term peace and security, he emphasized.
At last month's talks, Russia raised a list of tough demands, including calling on Ukraine to cede more territory and refuse all forms of Western military assistance.
Kiev has rejected these demands and questioned further negotiations as Russia is not ready to make transfers.
In early July, Russia said it was ready to continue negotiations with Ukraine after US President Donald Trump gave Russia 50 days to reach a peace deal or face sanctions.
Trump also pledged to provide new military aid to Kiev, which is funded by NATO allies.
Meanwhile, on the ground, Russia has intensified long-range airstrikes on Ukrainian cities as well as frontline and shelling attacks in recent months.
On July 19, Russia launched a missile and drone attack that killed three people across Ukraine.
Two people died after a Russian missile attacked the Dnipropetrovsk region, central Ukraine, a key industrial hub that Russian forces have recently advanced to.
Previously, a series of 20 Russian drones attacked the Ukrainian port city of Odessa, killing at least one person.
For its part, Russia had to suspend trains for about 4 hours overnight, leading to significant delays in the Rostov region of southern Ukraine, when the region was attacked by drones from Ukraine, injuring a railway worker.
According to the agreement reached during negotiations in Istanbul, Turkey, on July 17, Ukraine received 1,000 bodies of soldiers while Russia received 19 bodies from Ukraine.
On July 18, the European Union agreed on the 18th package of sanctions against Russia, targeting Russian banks and lowering the price ceiling for Russian oil exports.
