European Union governments will meet next week to discuss new rules that could open the EU’s 28 countries to more than 1 million refugees of the Ukrainian war. But, with a conceivably large number of people who may be looking to resettle permanently and a growing backlash against immigrants in many member states, the possible arrangement is creating controversy.

According to the agreement being discussed, Ukrainians could get visa-free travel into the EU by May. That is the same deal people in another ex-Soviet Union country, Moldova, have been enjoying since April last year as part of a program called Eastern Partnership. The EU is employing the program to forge closer ties with several former Soviet nations that could, one day, join the bloc. Besides Moldova, Ukraine and Georgia are also negotiating visa-free travel within the context of the partnership -- but, since the program’s inception, Ukraine has descended into a civil war and an economic crisis that make it a far less attractive prospect.

Moldova may be the poorest country in Europe, but it is at peace, and has just 3.5 million inhabitants compared with Ukraine’s 45. And it does not have more than  1 million internally displaced people driven from their homes because of a civil war.

One of the major fears of the EU interior ministers meeting next week is that opening their borders to Ukrainians could result in a large number entering with no intention of going back. Statistics show that’s exactly what has happened with some countries enjoying visa-free travel to the Union.

“There have been a couple of experiences in the western Balkans over recent years that have made interior ministers more hesitant to offer visa liberalization now,” said Elizabeth Collett, the Brussels-based director of the Migration Policy Institute Europe, a unit of an independent think tank headquartered in Washington.

The number of people from Albania, Bosnia, Macedonia, Montenegro and Serbia seeking asylum in the EU rose by 40 percent in the first nine months of 2014, compared with the same period the previous year, according to the European Commission, which has requested that the governments of those countries act to curb abuses. All five nations are participants in the visa-liberalization program, which allows the citizens of non-EU states to enter the bloc without obtaining visas.

“Many of those asylum claims were found to be unsubstantiated,” Collett said.

This finding has added to a lack of popular appetite for hosting vast numbers of refugees amid an economic crisis in the EU itself, where many see immigrants as competing for jobs, and unemployment has grown to an average of 10 percent from less than 7 percent when the crisis began in 2008. People entering the bloc under the visa-liberalization program are not automatically granted work permits.

“The benefits of visa liberalization have been very visible in terms of enhancing people-to-people contacts and business opportunities,” a European Commission report said in February. “However, misuse of the visa-free travel scheme for seeking asylum in the EU must be addressed systematically.”

Yet the issue of Ukraine’s participation in the visa-free travel initiative is unique and divisive.

“The great unknown is if the conflict escalates and starts moving west,” Collett said. “What will happen then? We’ll see a greater influx of people fleeing the conflict who are in need of protection within the European Union, and I’d expect the EU to respond accordingly -- to offer them at least temporary protection.”

The EU has been down that road before. During the Bosnian war in the 1990s, more than 1 million Bosnian refugees moved to countries throughout Western Europe. “Many of those people were offered temporary protection with the understanding that they would return home at the end of the conflict,” Collett said. “Certainly not a lot of those people did return home following the end of the conflict, nor had anywhere to return home to.”

The current arrangement for Ukrainians entering the EU is that they must apply for a visa from the country they wish to visit. Once inside the bloc, they can travel freely, as is the case under the rules of the Schengen Area, where the citizens of most EU member states can travel without passports.

The rise of right-wing parties opposed to immigration in several EU countries is another obstacle for Ukraine, which began talking about visa liberalization with Europe as long as seven years ago.

One such anti-immigration party is the Sweden Democrats, which won 49 out of 349 seats in elections last year with a platform that proposes cutting immigration by 90 percent -- in other words, pretty much eliminating it. Sweden is one of the countries that saw a big influx of refugees from the Bosnian war. The Sweden Democrats want Ukrainians to get help at home, and stay there.

“Europe, and Sweden in particular, have already today many challenges in regards to our societies as a consequence of our exceptionally large immigration from foreign countries,” Christian Krappedal, a representative of the Sweden Democrats’ youth organization, said via email. “We would like to see humanitarian aid more focused on the regional level and in the immediate area of concern as a means to help people in need. This also applies to Ukraine or any other country.”

Views such as these may not be translating to political majorities yet, but they are gaining traction. A Pew Research Center poll last year showed that in four of the seven large EU countries surveyed, most people said immigrants were a burden.

When EU government representatives meet at the Eastern Partnership summit in Riga, Latvia, in May, when any visa deals would be announced, they will be thinking of voters opposed to immigration. And that could be why this time, too, Ukrainians may witness another delay in the fulfillment of their hopes.

Citing “EU sources,” the U.S.-funded Radio Free Europe said Ukraine is unlikely to get visa liberalization at the May summit. The chances are better for the other candidate, Georgia, whose odds are given by those sources as an even 50-50. Then again, Georgia, whose own war with Russia was a short conflict in 2008, does not have 1 million potential refugees.