NEWARK — The fate of two New Jersey men who face sentencing this month on terror-conspiracy charges seemed headed for a legal slugfest Tuesday, despite the fact the two defendants have already pleaded guilty.

In a hearing to discuss the sentencing that’s shaping up to be a multi-day proceeding, attorneys for Mohamed Alessa and Carlos Almonte sparred with a government attorney over the significance of a fight that occurred in July between the two defendants and a third inmate at the Metropolitan Detention Center in Brooklyn, where they are being held.

Assistant U.S. Attorney Andrew Kogan indicated during the federal hearing in Newark that the government planned to make the fight central to its push for a tough sentence, arguing it showed the defendants remain likely to commit violence.

Stanley L. Cohen, an attorney for Alessa, demanded more information about the third inmate, who Cohen said had entered the defendants’ shared cell and attacked them. He hinted that the other inmate may have been motivated by prejudice.

Alessa, of North Bergen, was born in the United States and is the son of Palestinian immigrants. Almonte, of Elmwood Park, is a naturalized citizen who was born in the Dominican Republic.

Sitting in court Tuesday in handcuffs and prison scrubs, the two men spoke quietly to each other in Arabic. Alessa turned to smile and blow a kiss to his parents and other supporters who attended the hearing.

In March 2011, each pleaded guilty to conspiring within the United States to murder individuals outside the U.S. by trying to join al-Shabab, a designated terrorist organization.

Sentencing is scheduled to begin April 15.

U.S. District Judge Dickinson Debevoise said a video presented by the government of the fight at the Brooklyn jail was inconclusive, and questioned why prosecutors want to add it to the already voluminous pre-sentencing materials.

“To put more in at this late juncture is adding unnecessary debris to an already complex case,” Debevoise said.

The pre-sentencing report, which is said to be 1,000 pages or more, paints two different pictures of the men’s alleged motives, Debevoise added.

The judge asked Kogan for more information on the jail confrontation, including the criminal record of the other inmate involved. Debevoise also said he would allocate roughly two days for both sides to present their sentencing arguments, take a brief recess to write his own statement on the case, and then pronounce the sentences.

The charge Alessa and Almonte each pleaded to could carry up to life in prison, but they face 15 to 30 years under the terms of the plea agreement.

The two have been in custody since they were arrested in June 2010 trying to fly out of New York’s Kennedy Airport as they prepared to board separate planes to Egypt.

Alessa, who was 20 at the time, and Almonte, who was 24, admitted that they had planned to travel to Somalia to seek terror training from al-Qaida-affiliated jihadists. The men had no contact with Somali terrorists but hoped they would be accepted by a terrorist group, according to officials and court documents.

An undercover officer from the NYPD posing as a devout Muslim met Alessa, a Muslim by birth, and Almonte, a Muslim convert, in 2009 while circulating among men with radical leanings in the New York City area, according to investigators.

He got close enough to them to secretly record their radical rants about fighting a holy war here and abroad, authorities said.

While court documents seek to portray the men as deeply committed to terrorism, their training was apparently scattershot. They lifted weights, hiked in the snow at a local park, bought military-style pants and water bottles, played paintball and violent video games and watched terrorist videos online, the documents say.

Cohen has argued that his client — who was a teenager when law enforcement began surveillance on him in 2006 based on a tip he had been watching lectures by radical Muslim clerics online — was more of a troubled youth with mental health issues than a danger to society.

James Patton, who is representing Almonte, said he had conducted a coordinated defense with Cohen, and the two would continue that way for the sentencing.