Denmark has tightened controls at its border with Germany just hours after neighbouring Sweden introduced similar measures to stem the flow of migrants.

Danish Prime Minister Lars Loekke Rasmusssen told reporters in Copenhagen that police are conducting spot checks on travellers crossing the border from Germany.

"We are introducing temporary border controls, but in a balanced way," Mr Rasmussen said, adding there would be no problem for "ordinary" Danes and Germans to cross the border.

It was the latest move by a European Union country to suspend an agreement to keep internal borders open after one million migrants entered the bloc in 2015.

"If the European Union cannot protect the external border you will see more and more countries forced to introduce temporary border controls," the Danish prime minister said.

He said the Danish move was in response to new ID checks introduced by Sweden on Monday for all passengers entering the country by train, bus or ferry.

To comply with the new Swedish rules, passengers are having to show identification to board trains departing from Copenhagen Airport to Sweden across a bridge-and-tunnel link.

Danish officials have criticised the move and suggested Sweden should pay for the cost of the ID checks.

The Swedish government decided to tighten border controls after 160,000 people applied for asylum in Sweden last year - the highest number in Europe except for Germany. Most of them were from Syria, Iraq and Afghanistan.