Dozens of people have been killed in the onslaught, most of them civilians, a monitor has said, and many have been wounded
Obama made the comments to his Russian counterpart on the sidelines of an Asia-Pacific Economic Cooperation (APEC) summit in Peru, in what could be their last meeting before the US president leaves office in January.
It was the first time they had met since the US presidential election and the shock victory of Donald Trump, who has pursued a far warmer relationship with Putin than Obama did.
"On Syria, the president noted the need for Secretary (John) Kerry and Foreign Minister (Sergei) Lavrov to continue pursuing initiatives, together with the broader international community, to diminish the violence and alleviate the suffering of the Syrian people," said a White House official.
Syrian government forces last Tuesday launched a bid to retake the eastern rebel-held side of Aleppo using air strikes, barrel bombs and artillery.
Moscow, which began a military intervention in support of President Bashar al-Assad's government last year, says it is not involved in the current assault on Aleppo, instead concentrating its firepower on a neighboring province.
Around 250,000 people have been under siege in the eastern part of Aleppo, Syria's second city and its economic hub before the war erupted in March 2011.
Obama's comments came shortly after the UN's Syria envoy, Staffan de Mistura, warned that time was "running out" for eastern areas of the city, after talks in Damascus with Foreign Minister Walid Muallem.
Dozens of people have been killed in the onslaught, most of them civilians, a monitor has said, and many have been wounded.
In the four-minute conversation with Putin, Obama also urged Russia to uphold commitments related to the frayed Minsk peace accords which were aimed at ending conflict in eastern Ukraine.
"The president urged President Putin to uphold Russia's commitments under the Minsk agreements, underscoring the US and our partners' commitment to Ukraine's sovereignty," said the White House official.
Relations between Russia and the United States are at their lowest point since the Cold War, largely because of sharp differences over the conflicts in Syria and Ukraine.
Obama, who last met Putin at the G20 summit in China in September, is on his final foreign trip as president before handing over to Donald Trump on January 20.
Trump has expressed admiration for Putin, calling him a better leader than Obama and saying he would have a "very, very good relationship" with him.
Putin likewise complimented the Republican billionaire, calling him a "very bright, talented person."
During the campaign, US intelligence accused Russia of directing hacks to influence the election after sensitive emails from the Democratic party and Hillary Clinton's campaign were leaked.