The announcement came as Syrian rebels launched an assault on government forces to break a months-long siege of rebel-held eastern Aleppo.
"We have appealed to the Supreme Commander-in-Chief of the Armed Forces of the Russian Federation with a request to resume air strikes," senior military official Sergei Rudskoi told a briefing.
The Kremlin did not immediately comment on the ministry's request.
At least 15 civilians were killed and more than 100 wounded today by rebel rocket fire on government-held western Aleppo neighbourhoods, the Syrian Observatory for Human Rights said.
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The halt in bombing was initially declared ahead of a short ceasefire that ended at the weekend, with Moscow on Monday ruling out a truce extension for the time being.
Rudskoi added that Russia was ready to "assess any proposal about improving the humanitarian situation in Aleppo, including the introduction of 'humanitarian pauses'", but warned that a halt in bombing should not be used "for fighters to reach their objectives."
Russia has meanwhile denied any role in deadly air strikes on a Syrian school in the rebel-held province of Idlib that killed 22 children on Wednesday.
According to the Syrian Observatory for Human Rights, the strikes were carried out by "warplanes -- either Russian or Syrian.