Police in Hungary say increasing numbers of migrants are breaching a razor wire fence built to stop them crossing the border from Serbia.
In January, 550 people were caught getting through - up from 270 in December. More than 1,200 were caught in the first 20 days of February.
Hungary caused controversy with the 4m (13ft) barrier, completed in September.
However, several other countries have since introduced tough border controls to stop the influx of migrants.
The number of people crossing from Serbia dropped after Hungary built the fence along the 175km (110-mile) border with its neighbour last year.
But police say migrants are now increasingly getting through, mostly by cutting through or climbing over the barrier.
Most are from Pakistan, Iran and Morocco, who are no longer admitted through other routes.
It follows moves by Austria, Slovenia, and Balkan countries to limit the nationalities and the numbers of those being allowed through.
More than a million people arrived in the EU in 2015, creating Europe's worst refugee crisis since World War Two.
The majority of migrants and refugees have headed for countries like Germany and Sweden via Hungary and Austria after crossing from Turkey to Greece. Many are fleeing the conflict in Syria.
Far fewer migrants are entering Hungary than Austria but the sharply increasing trend of people breaching the border fence is alarming the authorities, reports the BBC's Central Europe correspondent, Nick Thorpe.
More people crossed from Serbia into Hungary in the first 20 days of February than in the same period in 2015, before a fence was even contemplated, our correspondent adds.
Once in Hungary, they face criminal charges or deportation.
Meanwhile Interior Minister Sandor Pinter has renewed the closure of three railway crossings to Croatia, for fear that migrants and refugees will again start walking down the tracks into Hungary.
On Friday Austria introduced a daily cap on the number of migrants and refugees allowed into the country.
Just 80 asylum applications will be accepted each day at the country's southern border, in a move condemned by critics as incompatible with European law.
The huge number of migrants and refugees arriving illegally in Europe has left countries struggling to cope and put the EU's Schengen passport-free travel zone at risk.
A note on terminology: The BBC uses the term migrant to refer to all people on the move who have yet to complete the legal process of claiming asylum. This group includes people fleeing war-torn countries such as Syria, who are likely to be granted refugee status, as well as people who are seeking jobs and better lives, who governments are likely to rule are economic migrants.