A thousand people demonstrated in the centre of Budapest on Tuesday against a fence Hungary is building along its border with Serbia to keep out an accelerating flow of migrants entering from the south.

The rally, organised by civic groups, started from the city's biggest church, Saint Stephen's, under banners reading "Jesus was a migrant, too" and "My best friend is a migrant".

The marchers walked to the neo-gothic Parliament building, where they demolished a 15-metre (16.4 yards) mock fence symbolising the one being put up along the border, cutting the wire into pieces.

The fence that Hungary started to construct on Monday will be four metres high and 175 kilometres (108.74 miles) long. The government says it is defending the European Union's and its own borders, after registering more than 70,000 migrants so far this year, up from 43,000 all last year.

The migrants come from poor or conflict-ridden countries like Syria, Afghanistan and Iraq. Most travel on to wealthier parts of the European Union, but under EU rules those states are supposed to send illegal migrants back to Hungary if that is where they entered Europe.

Speakers at the rally said the fence would not keep people from fleeing war zones and the money spent on it was a waste. One of them, Edit Gyantar said the fence was "immoral" after hundreds of thousands had moved into Western states from Eastern Europe for a better living.

"The money should be spent on aid," said Agnes Hars, a demonstrator.

A student from Germany, Johann Mahr, said all European nations had a responsibility to stop the suffering, "especially if it is caused by our foreign policy in the Middle East".

"These people are not economic migrants as the government says ... most of them are literally fleeing from situations that are absolutely horrible," he said.