White House Believes Vladimir Putin Coming Around on Assad’s Exit From Power

— -- ANTALYA, Turkey -- President Obama met with Russian President Vladimir Putin on the sidelines of the G20 summit in Antalya, Turkey today to discuss the conflict in Syria and the White House now believes Putin may be coming around on the point that Syrian President Bashar al-Assad must go, according to one White House official.

The White House says Russia now supports negotiations led by the United Nations on a transition government between the opposition and Assad regime that will lead to free and fair elections, according to the source. But Putin insists Assad should be allowed to run as a candidate. The White House disagrees.

Calling the 35-minute discussion "constructive," a White House official noted the meeting focused "around ongoing efforts to resolve the conflict in Syria," including Russia’s efforts to fight ISIS in Syria.

As the presidents sat in full view of cameras, Putin and Obama discussed at length today "a Syrian-led and Syrian-owned political transition" – in other words: what the U.S. sees as ultimately removing Assad from power – peacefully.

"President Obama and President Putin agreed on the need for a Syrian-led and Syrian-owned political transition, which would be proceeded by UN-mediated negotiations between the Syrian opposition and regime as well a ceasefire," the White House official added. "As the diplomacy continues, President Obama welcomed efforts by all nations to confront the terrorist group ISIL and noted the importance of Russia's military efforts in Syria focusing on the group."

While President Obama has publicly welcomed all nations fighting Islamic State, a White House source says that he stressed to Putin that Russia should target its bombs on ISIS, not moderates.

The Obama administration believes that since the downing of the Russian jet in the Sinai Peninsula on Oct. 31, which Obama "offered his deep condolences for the loss of Russian life," Putin is getting more in line with the international community's position that Assad must go.

The leaders did not have a formal bilateral meeting scheduled but the White House had hinted that an informal meeting was possible, similar to the circumstances leading to their impromptu meeting at the United Nations General Assembly on September 28.

ABC News' Patrick Reevell contributed to this report