BRUSSELS—More than three million Syrians may seek refuge in Europe if the regime of Bashar al-Assad prevails in Syria with Russian and Iranian help—making it essential that the European Union regains control over its external borders, European Council President Donald Tusk said on Tuesday.

“Today, millions of potential refugees and migrants are dreaming about Europe, not only from Syria, but also from Africa, Afghanistan, Pakistan, Iraq and other places. For all refugees, easy access to Europe and the lack of external borders have become a magnet attracting them to us,” Mr. Tusk, who presides over EU summits, told the European Parliament in Strasbourg.

Some 550,000 migrants and refugees have arrived in Europe since the beginning of this year, mostly via Turkey, Greece and the Balkan countries. But up to three million may be headed that way soon, as Russia and Iran’s involvement in Syria may tip the scale in favor of the Assad regime, Mr. Tusk warned.

“A potential victory of Assad’s regime is more likely today because of Iran and Russia’s engagement in Syria, and will result in the next migratory wave. According to Turkish estimates, another three million potential refugees may come from Aleppo and its neighborhood,” he said.

European governments and EU institutions have been scrambling for a coherent response to this unprecedented influx of people, some closing their borders then reopening them, Hungary erecting border fences and Germany briefly opening its doors to all Syrian refugees.

Mr. Tusk said Germany, which for more than a week had allowed free passage for migrants to enter the country, displayed “beautiful moral gestures which we all highly appreciate.” But now controlling the EU´s external borders was a precondition for an “effective, humanitarian and safe migratory policy.”

With German Chancellor Angela Merkel and French President François Hollande speaking jointly in the European Parliament on Wednesday, Mr. Tusk said he expects them to make a strong commitment for the protection of the EU’s external borders.

“Otherwise, they, and all of us, will become responsible for the re-emergence of walls and barriers on our internal borders, here in Europe. Europe without its external borders will become a breeding ground for fear in each and every one of us. And this will lead us, sooner than later, to a political catastrophe,” Mr. Tusk said.

With the migration crisis having pitted east against west, north against south, wealthier against poorer nations, Mr. Tusk said that “our internal disagreements and mutual recriminations only help our opponents.”

A former prime minister of Poland and an anti-Communist activist in the Solidarity movement, Mr. Tusk said that, while everyone in Europe likes talking about the need of solidarity and quotas for sharing the burden of refugees, few are appreciated when for calling for “responsibility and common sense.”

“It is our common obligation to assist refugees as well as to protect the EU’s external borders. Everyone must take up this obligation and at the same time no one should be left alone with the burden. That is how I understand solidarity,” he said.

“Let us have no illusions. Today, we have to count mainly on ourselves. The world around us doesn’t intend to help Europe. We are slowly becoming witnesses to the birth of a new form of political pressure, and some even call it a kind of a new hybrid war, in which migratory waves have become a tool, a weapon against neighbors. This requires particular sensitivity and responsibility on our side.”