COPENHAGEN (Reuters) - Denmark's populist anti-immigration party called on Friday for a referendum on the country's membership of the European Union following Britain's decision to leave, but the prime minister rejected such a possibility.

The Danish People's Party (DF), an ally of the right-leaning government, said it wanted a referendum about continued membership once Britain has negotiated the terms for its future cooperation with the union.

"I believe that the Danes obviously should have a referendum on whether we want to follow Britain or keep things the way we have it now," DF party leader Kristian Thulesen Dahl told broadcaster DR.

The DF is not in government but is one of three parties supporting the one-party administration. In total, the four parties have only one seat more than the opposition bloc. The DF holds 37 seats in the 179-seat parliament.

Its call for a popular vote was echoed by the head of the left-wing Red-Green Alliance. Those two parties hold 51 seats, while the minority government holds just 34 seats and depends on other parties to pass laws.

Prime Minister Lars Lokke Rasmussen rejected the calls, but acknowledged that the British vote raised the possibility of a "slimmer EU".

"We belong in the EU," Rasmussen told a news conference. "I do not foresee that there will be a situation in the foreseeable future where we need to take a break with that".

An opinion poll this week showed 59 percent of Danes would be against holding a referendum similar to the British on EU membership, while 33 percent were for a vote.

A spokesman for the biggest opposition party, the Social Democrats, holding 47 seats in parliament, told the same broadcaster that it was in Denmark's clear interest to remain within the EU.

The leader of Britain's UK Independence Party, Nigel Farage, said before the result was known that Brexit would trigger a domino effect in which several Northern European countries would leave the EU, starting with Denmark.

In Sweden, the anti-immigration party the Sweden Democrats has long demanded a referendum on the country's EU membership.

"The Sweden Democrats will now increase our pressure on the government, and we demand that Sweden immediately starts to renegotiate the (EU) deals we have made and that the Swedish people will be able to speak up about a future EU-membership in a referendum," party leader Jimme Akesson said by email.

In December, Danes voted and rejected adopting several EU justice and home affairs laws in order to stay within the cross-border policing agency, Europol.

(Reporting by Teis Jensen, additional reporting by Nikolaj Skydsgaard, Erik Matzen and Johan Sennero in Stockholm; Editing by Jacob Gronholt-Pedersen and Alison Williams)