She said the Skype conference began at about 10:00 a. m. Moscow time (7:00 GMT).
"I know for sure that [DPR envoy Denis] Pushilin and Kiev representatives are taking part," the aide said, adding a press briefing on the results of this linkup might be held later in the day.
Andrei Purgin, who is a parliamentary speaker in the self-proclaimed Donetsk People's Republic (DPR) in eastern Ukraine, said earlier on Tuesday negotiators were expected to bring up the issue of shortfalls in the newly-agreed ceasefire.
The Trilateral Contact Group, which gathered in Minsk to finalize the deal, included envoys from the Ukrainian government, eastern militias and Russia, with mediators from the Organization for Security and Co-operation in Europe (OSCE).
According to Purgin, the sides hope to discuss what they perceive as truce violations, including the failure to start the pullout of heavy weapons from the conflict zone, Kiev's blockade of the breakaway Donetsk and Luhansk regions, and humanitarian aid deliveries. He also accused Ukraine of blocking food deliveries to the DPR.
The ceasefire came into force on Saturday night. Heavy weapons were to be withdrawn at equal distances from the line of contact within two days.
But a spokesman for the Ukrainian military said Monday that government troops were not ready to pull back weapons due to continuing hostilities.