Croatia cannot rule out erecting a fence similar to Hungary's razor-wire barrier to manage the flow of migrants across its borders, the country's president told CNBC.

In an exclusive interview over the weekend, Croatian President Kolinda Grabar-Kitarovic left the door open to the prospect of a physical barrier after more than 200,000 migrants crossed into the Balkan country over the past month, according to police estimates.

On Friday, Hungary's right-wing government sealed off its southern frontier with Croatia after closing off its Serbian border last month, blaming the European Union for failing to agree on a plan to the stem the flow of asylum-seekers at its summit last Thursday.

"We have to admit that every country to protect its own borders. I don't look at this [Hungary's fence] as an act against anyone. The fact of the matter is that we have been flooded with migrant flows, and it has become very difficult to manage the flow of people," Grabar-Kitarovic told CNBC.

"I would like to avoid the situation where we have to put any kind of physical barrier on the border, but I have always requested from our government a tight control of the border... I don't know about the fence, I don't exclude it as a possibility in the future."

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She pointed to the potentially damaging impact of migrant flows on Croatia's economy as justification.

"We have committed to take care of about 1,600 people... so we are willing to invest in development. But we have just started to get out of recession, our GDP (gross domestic product) growth has just become positive in the last two quarters, we still have high unemployment... As much as we would like to help all of these people, we do have our limits."

As a result of Hungary's fence, Croatia has now begun rerouting people towards Slovenia, where they are expected to continue onto Western Europe, the preferred destination for most migrants. However, Ljubljana has already rejected Croatia's bid to send 1,800 people on a train after 2,100 people entered the country on Sunday, the Associated Press reported.

Any decision Croatia takes regarding borders will be coordinated with the rest of the European Union and determined according to migrant flows, the President said, adding that the crisis won't be ending anytime soon.