Slovakian Interior Ministry spokesman Ivan Netik told CNN his country's approach did not result from discrimination.
Instead, he said, it stemmed from concern over whether the migrants would stay in Slovakia for the long term.
Slovakia has only a tiny Muslim community, Netik said, and there are no mosques, making it hard for Muslims to integrate.
"That's the reason we want to mostly choose people who really want to start a new life in Slovakia," he said. "And Slovakia as a Christian country can really help Christians from Syria to find a new home in Slovakia."
A possible bottleneck in Greece
Meanwhile, Macedonia -- some 1,000 kilometers (more than 600 miles) to the south -- declared a state of emergency Thursday in its southern and northern border regions, the country's Interior Ministry said.
The decision clears the way for the country's army to help deal with the crisis.
At least 1,327 migrants, most of them Syrians, have expressed interest in applying for asylum over the past 24 hours, the Macedonian Interior Ministry said.
By doing so the migrants gain the right to spend three days in Macedonia until they apply for asylum. Most use that time to travel to the Serbian border, according to the country's state-run Macedonian Information Agency.
An estimated 44,000 migrants have arrived in Macedonia in the last two months, including 33,461 Syrians, the ministry said. The rest come from Afghanistan, Iraq, Pakistan and various African countries.
For migrants, crossing through Macedonia is the most dangerous part of the journey because of armed gangs and mafia. The migrants often wait until they are in large groups to cross safely.
Closing off Macedonia would create a bottleneck in Greece where, due to the economic difficulties there, the situation is considered unsafe for migrants.
'It's nothing against religion'
European Union member states agreed last month
to take in more than 32,000 migrants to ease the burden on Italy and Greece, where by far the largest numbers have arrived. Another 8,000 should be allocated by the end of the year, said Dimitris Avramopoulos, the European Union's commissioner for migration, who is Greek.
Most migrants who reach Europe are from Syria, Afghanistan and African nations, and they are fleeing conflict or poverty.
But Slovakia has made clear it is opposed to the idea of EU quotas on migrants.
"It's nothing against religion. It's not about discrimination. But it will be very false and insincere solidarity if we take now more than 1,000 people to Slovakia who don't want to live in Slovakia," Netik said.
"You can't force somebody to live somewhere. Most of them will leave in a few days to Germany, Great Britain or Scandinavian countries. It's not a solution. It's not help."
However, if Muslims do decide to come to Slovakia and apply for asylum, they will enter into the normal process, he said.
Germany expects 800,000 asylum seekers
At the same time, the German government said it expected up to 800,000 asylum seekers to come this year -- four times more than in 2014.
German Interior Minister Thomas de Maiziere published the revised forecast Wednesday.
The government had already registered 218,000 applications by the end of July, and de Maiziere's statement said there was no sign the trend would ease.
Past experience shows that the number of arrivals tends to be greater in the second half of the year. In addition, there's been a significant increase in migration through the Balkans and the Aegean Sea, leading to a dramatic escalation of the situation in Greece, the statement said.
Ministers from France and Britain met Thursday in the French port city of Calais to mark the signing of a new deal aimed at stemming the flow of migrants attempting to reach the United Kingdom illegally.
An increase in attempts has caused disruption to Channel Tunnel freight and passenger services and resulted in the death of a number of migrants.
"About 320,000 migrants crossed the EU external borders since early 2015," French Interior Minister Bernard Cazeneuve said.
"This involves, here in Calais, a strong migratory pressure, which causes firstly humanitarian problems. There are human tragedies we have to face involving people, women and children in vulnerable situations, but also migrants who die."
Slovakia: Tackle root causes
Netik warned that taking in migrants would not help with the causes of migration -- and that, if the wave of new arrivals does not stop, Europe could end up receiving millions of people.
Slovakia has been helping with the "humanitarian transfer" of migrants to other countries since 2008, he said. It has brought Syrian mothers and children from refugee camps in Turkey, for example, giving them food, health care, accommodation and schooling before sending them on, six months later, to their final destinations -- often the United States.
This number will be increased this year from about 300 to 500, he said.
Slovakia has also offered to house 500 people going through the asylum application process in Austria, starting in September, Netik said. They will be transferred from an asylum center in Gabčikovo back to Austria when the process is completed.
Many of the migrants have embarked on perilous journeys across the Mediterranean Sea from Turkey or North Africa, often in unseaworthy boats operated by human traffickers.
The U.N. refugee agency, the UNHCR, said Tuesday
that the number of refugees and migrants crossing the Mediterranean this year stood at some 264,500, including 158,456 to Greece, about 104,000 to Italy, 1,953 to Spain and 94 to Malta.