Obama floated the idea of joint action with Turkey to capture Raqqa during talks between the two leaders at a G20 summit in China, Erdogan said, according to Wednesday's edition of Turkey's Hurriyet daily, Reuters reported.
"Obama wants to do some things together concerning Raqqa in particular," Erdogan told reporters on his plane that arrived early on Tuesday, referring to terrorist group Daesh's self-style de facto capital.
"We stated that would not be a problem from our perspective. We said, 'Let our soldiers come together, whatever is necessary will be done'," the Turkish president said, adding that a specific Turkish role would depend on further talks.
His remarks come as Turkey is engaged in an incursion into Syria.
On August 24, Turkish Special Forces, tanks and jets backed by planes from the US-led coalition launched their first coordinated offensive in Syria. Damascus denounced the intervention as a breach of its sovereignty.
Erdogan said the operation, dubbed "Euphrates Shield," was aimed at “terror groups” such as Daesh and the Democratic Union Party (PYD), a US-backed Kurdish group based in Syria.
The PYD is the political wing of the Kurdish People's Protection Units (YPG), which Ankara says is an extension of the outlawed Kurdistan Workers' Party (PKK) fighting for autonomy in Turkey's southeast.
US officials have welcomed Turkish efforts to dislodge Daesh from Syrian strongholds but voiced concern when Turkish troops engaged fighters aligned to the YPG, a force Washington sees as a valuable ally in battling terrorists.
Turkish-backed forces clashed with YPG forces in the initial stages of the two-week old Turkish incursion into Syria, but have since shifted their focus onto territory held by Daesh and occupied a string of villages.
Turkey's military said late on Tuesday that three Turkish soldiers were killed when two tanks were hit by rockets fired by Daesh. Four others were wounded, it said.
Erdogan also said, "We do not have the chance to take a backward step. If we take a backward step terror groups like Daesh, PKK, PYD and YPG will settle there."
Turkey says it wants to establish a safe zone in the 98-kilometer (61-mile) area stretching from the town of Jarablus to the city of A'zaz in Syria.
Turkey says such a "safe zone" would help stem the flood of Syrian refugees. But the idea has yet to gain traction from the United States and Russia, both engaged in Syria, because of the military demands of policing such a zone.
The Turkish army sent 15 more tanks to a district near the Turkish-Syrian border, bringing the total number of tanks and armored vehicles in that area to 90, Turkey's Dogan news agency reported on Wednesday.
Syria has been gripped by foreign-backed terrorism since March 2011. Over the past few months, the Takfiri Daesh terrorist active in the Arab country have suffered major setbacks as the Syrian army has managed to liberate several areas.