Prosecutors did not reveal what Tsarnaev said, but they objected to what they called an attempt by Tsarnaev's lawyers to suppress the statement.
Tsarnaev, 20, has pleaded not guilty in the attack at last year's marathon. Two pressure cooker bombs were placed near the marathon finish line, killing three people and wounding more than 260.
Prosecutors have said they will seek the death penalty against Tsarnaev for crimes that include using a weapon of mass destruction.
Tsarnaev made the remark when an investigator working for his lawyers accompanied Tsarnaev's sister to a prison visit, a meeting that was monitored by an FBI agent, prosecutors said. The defense investigator started to explain to Tsarnaev's sister the rationale behind special restrictions placed on Tsarnaev in prison, prosecutors said.
They say Tsarnaev, "despite the presence of an FBI agent and an employee of the federal public defender, was unable to temper his remarks and made a statement to his detriment which was overheard by the agent."
The government described the conversation in a memo outlining its opposition to a request from Tsarnaev's lawyers to lift the prison restrictions, known as special administrative measures.
In a separate filing Friday, lawyers for Tsarnaev sought to have multiple charges against him dismissed, saying they are repetitive and that the total number of charges could sway jurors weighing whether to find him guilty and whether to sentence him to death.
They noted that more than half of the 30 federal charges carry a possible death sentence.
Experts have said earlier filings suggest the defense may try to save Tsarnaev's life by arguing he fell under the influence of his older brother, Tamerlan Tsarnaev , who died in a police shootout.
Tsarnaev's lawyers have also argued that the prohibitive prison measures limit Tsarnaev's interactions with people helping his defense team.
Prosecutors argued that the FBI agent's presence was permitted by the special administrative measures, which prohibit providing information to people outside the prison.
A judge agreed to ease some of the restrictions earlier, but Tsarnaev's lawyers filed a new request last week to lift them.
Miriam Conrad, one of Tsarnaev's lawyers, said their renewed request "was not prompted by any comment that Mr. Tsarnaev made during a family visit."
Tsarnaev's lawyers say the presence of the FBI agent during prison visits by Tsarnaev's two sisters "has thwarted the defense ability to develop important mitigation information."
Prosecutors have argued that the restrictions are necessary in Tsarnaev's case because of his "commitment to jihad" and his "widespread notoriety."
A spokeswoman for U.S. Attorney Carmen Ortiz declined to comment.
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