BRATISLAVA (Reuters) - Slovakia's far right People's Party launched a petition for a referendum on the country's EU membership on Saturday, the latest state to see a challenge following Britain's vote to leave the bloc.

Right-wing and anti-immigrant parties in the Netherlands, Denmark, Sweden and France have demanded referendums on membership of the union, while Italy's 5-Star movement said it would pursue its own proposal for a vote on the euro.

In Slovakia, which takes over the European Union's rotating six-month presidency in July, the anti-immigration, anti-euro People's Party-Our Slovakia shocked many in a March election when it won 8 percent of the vote, or almost 210,000 votes, to enter parliament for the first time.

"Citizens of Great Britain have decided to refuse the diktat from Brussels. It is high time for Slovakia to leave the sinking European 'Titanic' as well," the party said on its website.

Slovak law requires a petition to receive 350,000 signatures from the country of 5.4 million for a referendum to be held. The results of a referendum are legally binding if the turnout exceeds 50 percent of all eligible voters.

The only referendum that has been successful in Slovakia was the 2003 vote on its EU membership with a 52 percent turnout and 92.5 percent in favor of joining the bloc.

According to a Focus opinion poll released last week, 62.1 percent of voters would choose in a referendum to remain in the EU while 22.6 percent would vote leave in Slovakia.

Following the British vote to leave, Geert Wilders, leader of the Dutch anti-immigrant PVV party, said he would make a Dutch referendum on EU membership a central theme of his campaign to become prime minister in next year's parliamentary election.

France's far right National Front party also called for a referendum, cheering a Brexit vote it hopes can boost its eurosceptic agenda, as did the anti-immigration Danish People's Party (DF), an ally of Denmark's right-leaning government.

On Thursday, Britons voted to leave the 28-nation EU, forcing the resignation of Prime Minister David Cameron and dealing the biggest blow to the European project of greater unity since World War Two.

(Reporting By Tatiana Jancarikova; Editing by Toby Chopra)