BUDAPEST—Hungarian authorities struggled Wednesday to keep control of the tide of migrants hoping to head to Germany, as a standoff ground on at Budapest’s central train station and the overwhelmed city said it would open a new site to receive the hundreds who have converged there.

Hungary—on the periphery of the European Union—has been hit particularly hard by the crisis, but there were developments throughout the continent. Overnight, passenger train traffic in the English Channel tunnel was disrupted for hours after migrants were spotted on the tracks near the train station in Calais, France. Authorities in Austria and Hungary said they had rescued migrants who were being smuggled in vans.

The EU has been hard-pressed to handle the flow of desperate migrants, hampered by competing national interests and difficulty enforcing bloc-wide rules as migrants attempt to cross borders in search of better prospects in wealthier countries. The European Commission, the bloc’s executive, said Wednesday it would present proposals for a plan to share asylum seekers across the bloc before an emergency meeting Sept. 14, a key part of what Brussels hopes will be a more coordinated response.

Hungary has taken an especially tough tack, trying to restrict travel options for those without valid visas and enforce a European regulation that prevents migrants from seeking asylum in multiple jurisdictions. Authorities cleared out hundreds from Keleti international train station Tuesday, sparking a protest outside the building that continued through Wednesday as hundreds of demonstrators chanted “Freedom!” and “Germany!”

“I am hungry, I am thirsty, why can’t we go to the trains?” asked one 30-year-old, who said he was from Aleppo, Syria.