EU chief Jean-Claude Juncker spoke as Turkish forces launched an assault on Kurdish positions, with air strikes and explosions reported near the border.
Turkish President Recep Tayyip Erdogan announced the start of the attack, which is aimed at curbing the Kurdish-led Syrian Democratic Forces (SDF).
The SDF was previously allied to the US, which used it to crush the Islamic State group. President Donald Trump described Turkey's incursion into northern Syria as a "bad idea". Trump - who pulled US troops from the area in what was interpreted as a green light for Turkey to assault the Kurdish militias - insisted that Washington "does not endorse this attack".
The president said Turkey had committed to "ensuring no humanitarian crisis takes place - and we will hold them to this commitment".
Juncker told the European Parliament he recognised Turkey had "security concerns" along the border. But he warned the military action would not lead to a "good result", saying a political solution was the only way to end the Syrian conflict. "I call on Turkey as well as the other actors to act with restraint and to stop operations already, as we are speaking, under way."
"I have to say if the Turkish plan involves the creation of a so-called safe zone, don't expect the European Union to pay for any of it."
Ahead of the launch of the offensive, Russian President Vladimir Putin urged Erdogan to "think carefully" before taking any action.
The UN Security Council's president, South African ambassador Jerry Matthews Matjila, also appealed to Turkey to "protect civilians" and exercise "maximum restraint".
German Foreign Minister Heiko Maas said Turkey "is willingly risking further destabilising the region and a resurgence of IS" by attacking northeastern Syria. (AFP)