"They will be able to cross Croatia and we have been working intensively on that," Milanovic told lawmakers during a regular parliament session. "We are ready to accept and direct those people -- their religion and skin colour is completely irrelevant -- to where they apparently wish to go ... Germany, Scandinavia."
Milanovic spoke as earlier Wednesday some 150 Middle Eastern refugees crossed into Croatia from Serbia, its neighbour to the east.
"I don't approve the (migrant) policy of Budapest, I consider it harmful and dangerous. Not that the walls that are being erected will stop anyone, but they are also sending a horrible message. A fence in Europe in the 21st centry is not an answer but a threat."
President Kolinda Grabar-Kitarovic called a crisis meeting of the country's top security body, the National Security Council, which could be held either on Friday or next Tuesday.
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Its border with Serbia lies some 100 kilometres (60 miles) west of the capital Belgrade across flat terrain that is relatively easy to traverse.
Local media have warned of the dangers from mines remaining in the region from the Balkan wars of the 1990s.
More than 550 square kilometres (210 square miles) -- nearly one percent of Croatia's territory -- is thought to be riddled with mines left over from the conflict.
However Croatia's de-mining agency stressed that areas where mines remain are clearly marked with warning signs.
Since the start of the crisis the Croatian authorities have urged solidarity with migrants, recalling its own role in accommodating hundreds of thousands of refugees and displaced people during the 1990s Balkans wars.