Ushakov said that US special envoy Steve Witkoff and President Donald Trump's son-in-law Jared Kushner would be in Moscow "fairly soon" without specifying a date.
Ushakov said that the ceasefire, which runs until Monday, had been agreed over two days of phone conversations with the United States that he described as "not easy."
Witkoff and Kushner have mediated talks between Russia and Ukraine in the past without securing a breakthrough.
Ushakov noted that they had also been involved in talks on the Middle East conflict.
He repeated that Russia was ready to end the war if Ukraine withdrew from the Donbas region in the east of the country.
"In Ukraine, they know that they have to do that, and they will do it sooner or later in any case," Ushakov said.
Ukrainian President Volodymyr Zelenskiy has repeatedly rejected this demand.
Russian forces have thus far failed to take the strategically important cities of Kramatorsk and Sloviansk in Donetsk that Ukraine regards as key to defending the approaches to Kyiv.
Both sides reported widespread violations of the ceasefire that Trump announced on Friday although observers noted a general decline in attacks, particularly in strikes on energy facilities behind the front lines.
On Sunday, the Russian Defence Ministry reported more than 16,000 violations of the ceasefire including isolated gunshots.
It said that 57 Ukrainian drones had been downed.
Ukraine's general staff reported 150 Russian attacks and the air force said that 27 Russian drones had been downed.
Five people, including two children, were injured in the eastern Ukrainian city of Kharkiv when a drone struck a block of flats, the local authorities reported.
Zelenskiy said on Sunday that Russia had refrained from massive aerial and missile strikes on Ukraine since the start of a ceasefire but has not stopped attacks along the front line.
"It is nice that as of now, today there have been no massive attacks – missile strikes, air strikes," he said in his evening address on the second day of the pause.
"But there has been no peace in the frontline areas, in the communities near the front. The Russians continue their assault activity in those areas that are key for them."
with Reuters
