NEW YORK (Reuters) - Federal prosecutors on Friday urged a judge to lift her order barring enforcement of part of a new law that permits indefinite military detention, a measure critics including a prize-winning journalist say is too vague and threatens free speech.

Manhattan federal court Judge Katherine Forrest this month ruled in favor of activists and reporters who said they feared being detained under a section of the law, signed by President Barack Obama in December.

The government says indefinite military detention without trial is justified in some cases involving militants and their supporters.

But critics worry that the law is unclear and gives the Executive Branch sole discretion to decide who and what type of activities can be considered as supporting militants.

The judge's preliminary injunction bars the government from enforcing section 1021 of the National Defense Authorization Act's "Homeland Battlefield" provisions.

The section authorizes indefinite military detention for those deemed to have "substantially supported" al Qaeda, the Taliban or "associated forces."

In a brief filed in New York late on Friday, the government said the plaintiffs in this particular case had nothing to fear.

"As a matter of law, individuals who engage in the independent journalistic activities or independent public advocacy described in plaintiffs' affidavits and testimony, without more, are not subject to law of war detention as affirmed by section 1021," prosecutors in the Manhattan U.S. Attorney's office wrote.

During oral arguments in March, Forrest heard lawyers for former New York Times war correspondent and Pulitzer Prize winner Chris Hedges and others argue that the law would have a chilling effect on their work.

The judge said she was worried by the government's reluctance at the March hearing to say whether examples of the plaintiffs' activities - such as aiding the anti-secrecy website WikiLeaks in the case of Birgitta Jonsdottir, a member of parliament in Iceland - would fall under the scope of the provision.

Bruce Afran, a lawyer for the plaintiffs, said the government's brief failed to address fundamental concerns about what type of conduct is outside the law, and which person or group is deemed sufficiently "independent" of enemy forces.

"It is surprising that the government is pursuing this case because it has other statutes that specifically target terrorist groups," Afran said.

The government noted that courts rarely intervene in matters directed by the Executive Branch.

"Issuing an injunction regarding the President himself, or restraining future military operations (including military detention) ... would be extraordinary," prosecutors wrote, noting that they were considering an appeal of the judge's order.

(Reporting By Basil Katz; Editing by Xavier Briand)