The overall number of migrants fleeing war and poverty in the Middle East and Africa who entered the European Union member from neighbouring Serbia during the past 10 days totalled 65,000, an interior ministry statement said.
The influx started after Hungary sealed its border with Serbia earlier this month.
Most of the new arrivals were first accommodated in the recently-constructed refugee centre in the village of Opatovac, near the Serbian border. They were later taken on buses and trains to three border crossings with Hungary.
"The situation is under control," he added.
Meanwhile, Hungary's announcement that Budapest plans to eventually seal its border with Croatia in order to stop the migrant influx raised speculation people might take a new so-called southern route through Montenegro and Croatia.
Preparations were underway in southern Croatia in case there is a need to accommodate them, Ostojic said.
If the migrants do change route, Croatia may give them temporary shelter in military facilities remaining from the former Yugoslav People's Army in the Prevlaka peninsula, which is located at southern tip of Croatia's long coastline on the Adriatic Sea, 45 kilometres southeast of Dubrovnik, bordering Montenegro.
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