BOSTON — Prosecutors and lawyers for Boston Marathon bomber Dzhokhar Tsarnaev are sparring over whether an agreement that allowed a loosening of communications restrictions on Tsarnaev in prison should continue now that he has been convicted and sentenced to death.

After Tsarnaev was charged in the deadly 2013 bombing, his communications with the outside world were sharply limited, materials shown to him by his lawyers were inspected by prison officials and his visits with his lawyers were monitored.

In 2014, Tsarnaev’s lawyers complained that the measures were so restrictive they impeded their ability to prepare his defense.

The “special administrative measures” put in place for Tsarnaev have also been used in other terror cases and are designed to prevent suspects from communicating with others to incite violence.

Under an agreement between both sides, some restrictions were loosened. Prosecutors argue that the agreement is now “obsolete and unnecessary.”

Tsarnaev’s lawyers objected, arguing in court documents unsealed this week that the agreement was accepted by Judge George O’Toole Jr. and prosecutors cannot “unilaterally terminate” it.

The lawyers say prosecutors should not be allowed to obtain details about information shared between them and Tsarnaev while he was awaiting trial or going forward as they prepare his appeal.

Prosecutors, however, say they are entitled to review the records.

“The records in question are not privileged, confidential or work product. They are, on the contrary, records that are routinely obtained by prosecutors either automatically or upon request,” Assistant U.S. Attorney William Weinreb argued in court documents. “Tsarnaev is essentially asking this court to apply different rules to him than apply to the other 200,000-plus inmates in federal custody.

The judge has not indicated whether he will hold a hearing on the defense request.