"The early halting of air strikes is necessary to declare a "humanitarian pause", Mr Shoigu said in a televised statement.
Kremlin spokesman Dmitry Peskov said the halt was a "manifestation of goodwill" and denied it was meant to assuage western critics.
"We have taken a decision not to waste time and to introduce "humanitarian pauses", mainly for the free passage of civilians, evacuation of the sick and wounded and withdrawal of fighters", Sergei Rudskoi, a senior Russian military officer, said in Moscow.
Spokesman Jens Laerke of United Nations humanitarian coordinator OCHA said in Geneva the agency needs assurances from all sides that fighting will stop before it can provide humanitarian assistance to the city.
However, Russian and Syrian forces have only escalated their aerial and ground assault on the rebel-held areas in recent weeks.
Air raids have killed hundreds and caused worldwide outrage.
A Russia-US-brokered cease-fire last month collapsed as the Syrian army launched an offensive on eastern Aleppo under the cover of Russian warplanes.
Raids in the eastern neighbourhoods of Aleppo have stopped since the Russian announcement, but air strikes are still being conducted in the broader Aleppo region, the Britain-based monitoring group Syrian Observatory for Human Rights said Tuesday.
"There were airstrikes throughout the night", Abu Rajab, who works at a local hospital, said over the telephone.
More news: Called Third Strike: Giants' Bochy in no-win situation in 9th against CubsThey had no immediate word on casualties.
Shoigu urged the countries wielding influence with the rebels in Aleppo to persuade them to leave the city.
Shoigu said Russian Federation expected opposition fighters to leave via two corridors - Castello Road and Al-Khai Souq market - and that Assad troops would retreat to allow them to leave with their weapons.
The Russian initiative should also boost talks between military experts from several nations that are set to open in Geneva on Wednesday, he added.
Repeated efforts to separate moderate fighters from al-Nusra have so far come to nothing, partly due to resistance in Aleppo, and the lack of assurances about the length of the ceasefire.
Russian Federation is calling on countries with influence on Syrian opposition groups to intensify efforts to separate moderate forces from terrorist entities in besieged eastern Aleppo in a draft statement submitted to the U.N. Security Council on Tuesday.
Russian and Syrian officials have since embraced a proposal made earlier this month by the UN Syria envoy, Staffan de Mistura, to allow Al Qaeda-linked militants to leave Aleppo in exchange for a truce and a local administration for the eastern districts.
"A new massacre happened this morning when Russian warplanes bombed the Marjeh neighbourhood killing 14 people from the same family, a lot of them women and children", Ibrahim Abu Leith, Aleppo-based spokesman for the White Helmets, told Al Jazeera on Monday.
At least 14 members of one family have been killed in an air strike on rebel-held east Aleppo in northern Syria, bringing the death toll to 47 over the past 24 hours.
The source said that several Iraqi government troops were killed by an IED on Tuesday along the southern frontline of the battle. Ajgeiy praised recent success of the joint forces that recently managed to regain control over some 80 square miles in Mosul.
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