Luhansk's governor says poor weather is stalling the project.
The drills involve Russia's Southern Military District, which covers Black Sea and Caspian territories.
The group allegedly attacked a march in memory of Ukrainian soldiers killed in bordering Donetsk and Luhansk.
Last week, Amnesty International warned that the country was heading for a "humanitarian catastrophe".
Ukrainian president Petro Poroshenko confirmed the meeting at a press conference on Monday
Though a cease-fire was reached with one group, another separatist group attacked the Donetsk airport.
Report gives detailed accounts of harassment by pro-Russian militias of Ukrainian media, anti-Russian activists and Muslim minorities
A Ukrainian spokesperson denies incursion can be called an invasion as Kiev sources report internal turmoil between pro-Russian forces
Reporting from both sides of the makeshift border in eastern Ukraine, Newsweek describes the bloodshed that has occurred inside rebel-held Ukraine