The local ceasefire came hours after US Secretary of State John Kerry warned Moscow that Washington's patience was running out over breaches of a nationwide truce.
Aleppo has seen some of the worst fighting in a war that has killed more than 280,000 people, but there is deep scepticism that the latest halt to fighting in the northern city will last.
Peace talks aimed at ending the five-year conflict have stalled and the February 27 countrywide ceasefire between the regime and non-jihadist rebels lies in tatters.
He accused Washington, which supports Syrian rebels, of being "unable or unwilling to put pressure on its allies in the region".
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Nevertheless, direct contact between Russia and the United States about Syria have taken place "without any hysteria", he added.
There have been repeated violations of the February 27 truce in Aleppo, with rebels pounding regime-controlled neighbourhoods with rocket and artillery fire and the regime hitting rebel areas with air strikes.
The new 48-hour ceasefire was announced by Moscow late Wednesday in a bid to halt violence in the city, split since 2012 between a regime-held west and a rebel-controlled east.
The statement did not specify who Russia has discussed the two-day ceasefire with.
Residents in Aleppo's rebel-held east headed out to the markets to buy meat and vegetables on Thursday morning, an AFP reporter there said.
After weeks of air strikes, it was the first time they have shopped in the morning since the start of the holy Muslim month of Ramadan.
But a Syria analyst, Karim Bitar, described the latest local truce in Aleppo as a "ceasefire of convenience, which is not linked to a real political process".