PARIS (Reuters) - French labor unions on Tuesday rejected government demands they cancel a protest march through the streets of Paris, raising the specter of a showdown with riot police in less than 48 hours.

Interior Minister Bernard Cazeneuve, who last week threatened to ban the rally after running battles between police and rioters on the fringes of previous protests, told parliament that he would make clear the government's position shortly.

The Socialist government is torn between the potential political fallout from prohibiting the march and the risk of violence at a time when police are stretched securing the Euro 2016 tournament under a state of emergency.

The militant CGT union and six others behind the demonstration slated for Thursday stood their ground after meeting police officials who said they could hold a stationary rally in a Paris square but not a march through the streets.

"The unions ... categorically rejected this proposal, noting that protest is a constitutional right and that it is up to the state to ensure security at all protests in public areas," said a statement signed by the unions involved.

Trade unions and students have for months been protesting against plans to loosen France's strict labor laws that opponents of the bill say protect workers's rights. President Francois Hollande says liberalizing the labor market is the best way to tackle double-digit unemployment.

"We're not seeking to ban the protests," Interior Minister Bernard Cazeneuve told reporters. "We're seeking to ensure that protests do not present a risk of violence. The police are tired and need some recovery time."

The government has the right to ban public protests on grounds that there is a serious risk to public order and has broader powers to do so under the emergency rules in force since Islamist militants killed 130 people last November.

Defiance of a protest ban would expose organizers to fines and up to six months in jail.

Imposing a ban would nonetheless require the mobilization of large numbers of riot police to enforce it.

During a June 14 protest, hundreds of mostly masked rioters ransacked shop fronts, clashed with police, tore up street paving and smashed the windows of a children's hospital during running battles in Paris. Police responded with tear gas and water cannon and dozens were hurt on both sides. [L8N1972QA]

(Reporting By Brian Love; Editing by Richard Lough and Dominic Evans)