Police said 9,380 people were caught crossing from Serbia on Monday
More than 150 refugees have been detained in Hungary, after the country sealed off its border with Serbia and declared a state of emergency.
A vast razor-wire fence has been constructed between the two countries, as huge numbers of refugees try to reach the European Union.
Austria says it'll also introduce tougher border controls tonight.
Hungary also declared a state of emergency in two southern counties near the border because of the migration crisis.
The Hungarian army has already been deployed in the south of the country? but reinforcements may be sent to the crisis areas.
On Tuesday, police detained the 60 migrants for breaching the razor-wire fence, the government said. The spots where the fence was damaged were being repaired.
Police also said 9,380 migrants were caught crossing from Serbia on Monday, the highest daily figure this year.
The government has vowed to build a 3.5m-high fence across the entire 108 miles of Hungary's southern border by October.
New border laws and powers to expel asylum seekers who cross from Serbia were enacted at midnight local time, prompting hundreds of people to camp out at the border, as aid workers brought tents, food and water.
The Hungarian government has been criticised for its treatment of the refugees, but insists it is doing what is necessary.
Hungarian ruling party MEP György Schöpflin spoke to Lunchtime to explain Hungary’s stance on this, and insisted roughly “two-thirds” of the Hungarian public are backing their government is doing, believing it is “harsh but correct”.
Listen: Hungarian MEP György Schöpflin speaking to Newstalk Lunchtime
“There has been a vociferous minority which says refugees are good, but ... two-thirds are saying ‘what the government is doing is right’,” he said.
“It’s deeply shocking for any country where suddenly it is overwhelmed that thousands of people are passing through the country like it doesn’t exist.
“How can you have law and order? How can you have democracy?
“On the whole they are saying, yes what the government is doing is harsh, but correct”
Peter Spiegel is the Financial Times' bureau chief in Brussels.
He told the Pat Kenny Show here on Newsralk the latest crackdown in Hungary has not come as a major surprise.
But officials are adamant the country has the right to protect itself, while also claiming it is ensuring the integrity of Europe's borders.
The United Nations refugee agency, the UNHCR, said it disputes Hungary's designation of Serbia as a "safe third country", and advised migrants against returning to Serbia.
More than 190,000 refugees have been recorded as entering Hungary this year, many of them fleeing civil war in Syria.
Most of the refugees are trying to reach the richer countries of northern and western Europe, particularly Germany.
Hungary says refugees are still able to claim asylum at official border crossings, but if they have entered from Serbia they face automatic expulsion within eight days.
Any refugee attempting to enter the country unofficially faces a 12 month to three-year prison term.
At the official border crossing, around a mile from the now-closed unofficial crossing point, the Hungarian authorities launched an unexpected mass transit operation.
Refugees still inside Serbia were allowed to form themselves into lines and enter the customs area, to be loaded onto buses.
They were then driven a short distance to trains waiting to take them to Austria.
Hundreds of thousands of refugees have made the journey to Europe this year, the vast majority heading to Germany, as they flee conflict and poverty in the Middle East and Africa.
In Brussels, ministers from the 28-nation bloc have agreed to share responsibility for 40,000 people seeking refuge in overwhelmed Italy and Greece.
The leaders are hopeful of reaching eventual agreement on which European nations would take 120,000 more.
The European Commission wants 22 EU member states to sign up to a quota policy - but several nations oppose such a move, including Poland, Slovakia and Hungary.
Ministers will meet again next month to work out how many refugees each nation will take in. But the failure to reach a consensus on the 120,000 has drawn criticism, including from some aid agencies.
The German Vice Chancellor Sigmar Gabriel said "Europe made a fool of itself again yesterday." Mr Gabriel raised the projection on the number of newcomers Germany expects to shelter this year from 800,000 to one million.
Petros Fassoulas is the secretary-general of European Movement International. He told Newstalk Breakfast we have the means to help these people - as well as the weaker member states.