But Turkey, which already hosts some four million refugees, is trying to hold off another mass influx from Syria where regime forces, backed by Russian air power, are advancing into the last rebel stronghold of Idlib.
Erdogan said he hoped for a ceasefire in Syria when he meets his Russian counterpart Vladimir Putin later this week. But he warned Europe that it would share the migrant pressure. "After we opened the doors, there were multiple calls saying 'close the doors'. I told them 'it's done. It's finished. The doors are now open. Now, you will have to take your share of the burden'," he said.
Erdogan claimed the numbers of migrants at the Greek border, who include Afghans, Syrian and Iraqis, were far higher than figures provided by officials and reporters at the scene. He said there were already hit "hundreds of thousands" there.
"There will be more. Soon, this number will be expressed in millions."
Greece says some 10,000 were barred from entering the country over the weekend. Clashes broke out as police fired tear gas at the refugees who responded by lobbing rocks.
A video shared by a Turkish official, which could not be independently verified, showed a boat of migrants being shot at and harassed by Greek coastguards.
Turkey also accused Greek police of killing a migrant after a video was shared of a bloodied Syrian on the border, although Athens rejected this as "fake news".
In desperation, many have sought alternative routes and Greek port police said a young boy died when a makeshift boat capsized off the Greek island of Lesbos.
Athens said it would boost patrols and it suspended asylum applications by those entering illegally - a move denounced by the UN refugee agency as having "no legal basis".
Turkey agreed in 2016 to stop refugees leaving for Europe in exchange for billions of euros in assistance, and the EU insists that Turkey stick to the deal.
The migrant question comes as Turkey has launched a military operation in Idlib in northwestern Syria in a bid to push back the regime's offensive.
Close to one million people have been forced to flee the regime's assault in the biggest wave of displacement of the nine-year conflict, but they are not being permitted into Turkey. Erdogan and Putin are to meet in Moscow on Thursday.
Despite being on opposing sides of the conflict, they are keen to avoid direct clashes that would jeopardise their broader trade and defence ties. "I hope that he (Putin) will take the necessary measures there, such as a ceasefire, and that we will find a solution to this affair," Erdogan said in a speech Monday.
The Kremlin said cooperation with Turkey was a top priority.
"Our militaries are in constant contact. The main thing is that we now focus on negotiations between Putin and Erdogan," a spokesman said.
Turkey backs certain rebel groups in Idlib and has observation posts under a 2018 deal with Russia that was supposed to prevent a full regime assault. But the Syrian regime has made steady progress since December, and on Monday, retook the town of Saraqeb, according to the Syrian Observatory for Human Rights, a Britain-based war monitor.
Tensions between Turkey and Syria reached new heights last week when 34 Turkish soldiers were killed in an air strike blamed on Damascus, its heaviest loss since it first intervened in the conflict. "The airstrikes... were likely committed by the Russian air force, as Syrian fighter jets do not conduct air sorties at night," said Anthony Skinner, of analysts Verisk Maplecroft. "And yet, both Moscow and Ankara have decided to point the finger of blame at (Syrian President Bashar) al-Assad, reflecting how little appetite there is on either side for more direct confrontation."
Turkey retaliated with an operation that saw two Syrian warplanes shot down on Sunday, as well as at least 19 Syrian soldiers killed in drone strikes.