By Krisztina Than and Justyna Pawlak

BUDAPEST - Hungary is ready to build a fence on its border with Romania "the next day" if migrants switch to that route instead of going via Croatia, Hungary's foreign minister said on Tuesday.

Peter Szijjarto told Reuters the southern frontiers of Europe were still wide open to the continuing influx of hundreds of thousands of migrants from the Middle East and Africa, which has put in doubt the future of the Schengen system of open internal borders within the EU.

He said it would require tens of thousands of police and troops in a joint European force to stem the flow of migrants at Greece's long maritime borders.

"If it was not tragic I would laugh when I hear European officials speaking about hundreds of Frontex officers being the solution - it's not the case," Szijjarto said in an interview.

"If Greece is not willing to take part in this solution ... we need the Bulgarians and Macedonians to talk to."

The EU's border agency, Frontex, said last month it would increase its presence in Greece to better handle the influx of migrants crossing the Mediterranean into Europe.

The EU plans to nearly treble its spending on frontier defense and create a 1,500-strong rapid reaction force to replace Frontex.

Hungary's pugnacious Prime Minister Viktor Orban has gained public support with his tough stance on migration. His right-wing government has put up steel fences on the country's southern borders with Serbia and Croatia to keep out migrants fleeing war and poverty in the Middle East.

The barriers initially drew criticism from European Union partners, but other countries, such as Slovenia and Austria, have since erected fences of their own.

BOTTLENECKS

Szijjarto said Hungary had made preparations for a fence to be built quickly on its border with Romania if necessary.

"If we have to build a fence there, we are ready from the next day," he said.

Austria said on Friday it would deny entry to migrants intending to pass through to Germany rather than apply for asylum there, prompting Slovenia to its south to announce a similar move, to avoid becoming a refugee bottleneck.

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This could turn Romania into a popular route later this year. From Romania, migrants would be likely to try to enter Hungary en route for western Europe.

"It is more likely than ever that the southern border of the Schengen zone will be equal to the northern border of Greece (with Bulgaria and Macedonia)," Szijjarto said.

Czech Prime Minister Bohuslav Sobotka expressed a similar view on Tuesday, saying the EU needed a "back-up" border control system ready in case migration could not be controlled in Turkey or Greece.

The Schengen system has already been suspended on some EU frontiers. Few migrants have passed through the Czech Republic so far, but that could change if Germany, the desired destination for most, sealed its borders.

"We need to strengthen the outer Schengen border, to create a common European border patrol," Sobotka told reporters.

"And if nothing of this works, then we have to create a back-up border system on the Bulgaria-Macedonia line."

(Editing by Andrew Roche)