BRATISLAVA (Reuters) - Slovakia's parliament on Tuesday acted to curb patrolling of trains by far-right vigilantes who have been accused by rights activists of stirring racial hatred, but the group threatened to extend its patrols to other parts of the country.

Members of the People's Party-Our Slovakia, wearing green T-shirts and some carrying legally-held weapons, have been patrolling irregularly on trains since a 21-year old girl was assaulted and robbed in April.

The anti-immigration, anti-euro opposition party says the attack showed the inadequacy of the police to ensure passengers safety, but rights groups say their activities are aimed at Slovakia's Roma minority.

The center-left government and the national railway company have tried to end the patrols but say they lack the legal means to evict vigilantes if they hold valid tickets and do not bother passengers.

A legal amendment approved by parliament on Tuesday ruled that only the police or the train operator were responsible "for public order and protection of rights, lives, property and health of the commuters".

But People's Party said the patrols would continue and even be extended to other parts of the country.

"People in eastern Slovakia are being terrorized by asocial parasites," lawmaker Milan Mazurek in charge of the patrols said in parliamentary debate on the amendment.

"When the patrols are in trains, all passengers behave better, we did not have to use force so far, our presence is enough," he told Reuters.

The People's Party entered parliament for the first time last March when it won huge support for its anti-immigration program as Europe struggled to handle the flood of migrants from Middle East war zones.

Slovakia has not been a principal route for the migrants. But critics of People's Party say the party has capitalized on popular disenchantment with the European Union as it struggles to deal with several crises to target the Roma minority. Roma account for around 300,000 of the 5.4 million population.

The party, whose support stood at 8.3 percent in September, has also launched a petition to hold a referendum to leave the EU and NATO.

(Reporting By Tatiana Jancarikova; Editing by Richard Balmforth)