The European Union predicted Thursday that up to 3 million additional asylum seekers could enter the 28-member bloc by the end of next year, suggesting the staggering pace of new arrivals in recent months shows no sign of abating.

The forecast, buried in a 204-page report on the future of the European economy, will add to an already burning debate in Europe about whether the continent can handle the influx, which has broken all modern records.

So far this year, more than 760,000 people have entered the continent seeking refuge or jobs, according to the U.N.’s refugee agency. The new arrivals have badly strained government resources in countries all along the trail, which leads from the Mediterranean Sea in the south to richer nations in Europe’s north.

One of the more affluent countries, Sweden, said Thursday that it would apply for emergency E.U. aid, an admission that it is failing to cope. Sweden, which has taken the largest per capita share of refugees of any E.U. country, is expecting 190,000 asylum seekers this year — double its previous record.

“The major problem today is that the number of asylum seekers is growing faster than we can arrange for accommodation,” Morgan Johansson, the minister for justice and migration, told reporters. “Sweden can no longer guarantee accommodation to everyone who comes. Those who are arriving could be met with the news that there isn’t anywhere to stay.”

The Swedish Migration Agency said it would house 50 migrants in its headquarters, having run out of space in hotels, apartment buildings, tents, old army barracks and converted prisons.

Despite the strain, Thursday’s European Commission report predicted a modest overall economic boost from the migrant influx, citing higher government spending and an expanded labor pool.

“If managed properly, the inflow of refugees will have a small favorable effect on growth in the short and medium term,” the report concluded.

That view is deeply controversial in Europe, which has been polarized by the crisis. Viktor Orban, the nationalist prime minister of Hungary, said Thursday that Europe needs to encourage its citizens to have more children instead of welcoming refugees from South Asia, North Africa and the Middle East. “The survival of our civilization and our culture is at stake,” he told a conference.

The prediction of 3 million additional asylum seekers by the end of 2016 was based on an expectation that the pace of arrivals will remain in line with the extraordinary levels experienced in Europe in recent months. The numbers were not forecast to decline until 2017.

Despite the unprecedented scale of the flows, the overall population of the European Union was forecast to rise only 0.4 percent as a result of the influx.

In a separate forecast, the U.N. High Commissioner for Refugees said it predicted that an average of up to 5,000 migrants a day would travel from Turkey to Greece over the next four months. That would mark a substantial departure from the migrant travel patterns in previous years, when winter’s harsh weather vastly reduced the numbers.

The refu­gee agency appealed for nearly $100 million to winterize tents and sanitation systems while it warned of more deaths among refugees “if adequate measures are not taken.”

Peter Sutherland, the U.N. secretary general’s special representative on migration issues, told the BBC that there was no sign that the flow of migrants was diminishing, despite a rising death toll from rougher autumn seas. He called for Europe to take collective action to deal with the crisis.

“This is now a global responsibility, but it is a particular European responsibility,” he said. “And in Europe we can’t say simply that those who are the closest to the problem, and therefore receive most of the migrants, have to handle it themselves.”

Countries up and down the migrant route reported Thursday that they had received record numbers of asylum applications in the previous month. Germany said 181,000 people had applied for sanctuary in October, 17,000 more than in September. About 750,000 people have sought protection in Germany this year. Austria said asylum applications were up 231 percent over last year.

Meanwhile, there were several close calls on the high seas — along with more deaths.

Spain’s Defense Ministry said its forces­ had rescued 517 people from a wooden fishing boat that was adrift off the Libyan coast. The Greek coast guard reported that it had pulled 78 people from a wooden boat that had run aground off the island of Kos, while 293 people were rescued from inflatable dinghies off the coast of Lesbos. The Greek coast guard was searching for the body of a 6-year-old boy and had recovered the body of another child after their boat overturned near Kos.

“I think we are battling something that is beyond our abilities, and everyone should understand that,” Greek Prime Minister Alexis Tsipras said on a visit to refugee reception centers in Lesbos. “It’s an asphyxiating situation.”

Read more:

Why the language we use to talk about refugees matters so much

As tragedies shock Europe, a bigger refugee crisis looms in the Middle East

Read The Post’s coverage on the global surge in migration