"Welcome UN Security Council condemning execution of democracy activists", said the "National Unity Government" (NUG) on a verified Twitter account.
It was time for the council to "take concrete actions against the junta, it added.
The NUG -- dominated by lawmakers from Aung San Suu Kyi's ousted party -- has been working to topple the coup and been declared a "terrorist" organisation by the junta.
The executions announced Monday sparked condemnation from around the globe, heightened fears that more will follow and prompted calls for sterner international measures against the already-isolated junta.
Among the four executed were Phyo Zeya Thaw, a former lawmaker from Suu Kyi's National League for Democracy (NLD) and veteran democracy activist Kyaw Min Yu -- better known as "Jimmy".
Both were sentenced to death under anti-terrorism laws.
The junta is increasingly isolated on the world stage, with Cambodian leader Hun Sen the only head of state to have visited since the coup that plunged the country into turmoil.
The Cambodian PM had also made a personal request to junta chief Min Aung Hlaing not to go ahead with the executions.
Myanmar's junta has lashed out against international condemnation of its use of capital punishment, saying the four executed prisoners "deserved many death sentences".