The two met Thursday in Washington as efforts to bring the Assad regime and the Syrian opposition together at an international conference next month gathered pace.
At a joint White House news conference, the Turkish and US leaders restated their position, but Obama admitted: "There is no magic formula for dealing with an extraordinarily violent and difficult situation like Syria's."
World leaders have been beating a path to Moscow's door in recent days, amid hopes that Russia can sway the Assad regime to come to negotiations, and end the killing which rights activists say has claimed some 94,000 lives.
Russian President Vladimir Putin was to meet UN Secretary-General Ban Ki-moon on Friday as French President Francois Hollande said greater efforts were needed to convince Moscow to drop its support for Assad.
"We must have a frank discussion with Russia to convince it that it is in its interests, in the interests of the region, in the interests of peace, to finish with Bashar al-Assad," Hollande said.
Jordan, meanwhile, announced it would host next week the "Friends of Syria" group, bringing together foreign ministers from 11 key countries including Egypt, Qatar, the United States, Britain, France, Turkey and Germany.
Top political directors from the US, Britain and France also held low-key talks in Washington Thursday to prepare for the planned peace conference.
Even as Obama and Erdogan were meeting, Israeli officials told AFP that John Brennan, director of the US Central Intelligence Agency, had also arrived in Israel for talks on the Syrian crisis.
Obama has made strenuous efforts to court the Turkish leader but there are signs of frustration in Ankara, which is struggling under a tide of Syrian refugees, at Obama's cautious approach on Syria.
The president has balked at providing arms and ammunition to the guerrillas, fearing they could fall into the hands of extremist elements linked to Al-Qaeda.
After meeting Erdogan, Obama gave no sign his position has changed.
"We both agree that Assad needs to go. He needs to transfer power to a transitional body," he said. "That is the only way we're going to resolve this crisis."
Earlier a Turkish official told AFP Erdogan would push for direct US military aid for the rebels.
"Everyone in the international community is very much concerned, worried about the radical elements," he said.
"We are of course concerned more than anyone else, being a neighbor of Syria -- but the way to deal with that problem is not withholding your support. Not doing anything is not a solution."
Obama has said Washington has a moral and national security incentive to stop the killing, but has demanded more evidence to stand up reports that Syrian forces have used chemical weapons, crossing a US red line.
Turkey also seems skeptical that the peace conference Washington is planning with Assad's main ally Moscow will lead to a roadmap to a political transition.
"We have to be... realistic and very careful as to not turn this into an open-ended process which would give the opportunity to the regime to gain time and to continue its campaign of violence," the official said.
Despite their joint peace push call, a vote on Wednesday at the United Nations underscored the lingering divide between Washington and Moscow.
Russia voted against a motion before the UN General Assembly to condemn what Arab and Western powers denounced as Assad's "escalation" in attacks on civilians.
The vote passed despite Russian anger, but the number of states backing the motion was only 107, down from 133 when a similar vote was held in August.
In another sign of the tensions, attackers briefly abducted three UN peacekeepers in the Golan Heights, a top UN official said Thursday.
UN peacekeeping chief Herve Ladsous said the three unarmed UNTSO observers "were taken and held for approximately five hours and were released unharmed." He did not give their nationalities, but at least one was said by New Zealand media to come from their country.
It was the third abduction of UN forces in the Golan zone in two months.