Civil liberties advocates have said a suspect should rarely be questioned without a lawyer and without being told he doesn't have to respond.
"Miranda rights are an incredibly important civil liberties safeguard," said Hina Shamsi of the American Civil Liberties Union. "The public safety exception must be read narrowly, as it has been by the courts."
But California Democratic Rep. Adam Schiff, a former federal prosecutor, said he has questions about how the court proceeding came about.
"I would have thought the public safety exception would have allowed more time for the questioning of the suspect prior to the arraignment and/or advising of rights," Schiff said.
Based on the younger man's interrogation and other evidence, authorities have said it appears so far that the brothers were radicalized via Islamic jihadi material on the Internet instead of any direct contact with terrorist organizations, but they warned it is still not certain.
The brothers are ethnic Chechens from Russia who came to the United States about a decade ago with their parents. The family was granted asylum.
The chairman of the House Judiciary Committee said Thursday that the way the U.S. grants asylum to immigrants may need to be addressed after the marathon bombings.
"People getting asylum because they are in the minority, but engaging in aggressive tactics in their home country that may cause them to be susceptible to doing the same thing elsewhere, that obviously ought to be a part of our consideration in granting political asylum to avoid situations like Boston," said Rep. Bob Goodlatte, R-Va., who's working to develop a series of bills to fix problems with the country's immigration system.
Homeland Security Secretary Janet Napolitano defended the asylum process this week in an appearance before the Senate Judiciary Committee, saying it involves multiple layers of vetting.
A comprehensive immigration bill introduced last week in the Senate also may undergo changes in response to Boston. One of its authors, Sen. Lindsey Graham, R-S.C., has suggested strengthening background checks done on certain immigrants considered higher-risk, such as refugees or asylum-seekers.
In New York, Kelly and Bloomberg said they were briefed on the New York plot on Wednesday night by the task force investigating the Boston bombing.
Rep. Peter King, R-N.Y., said in a CNN interview that the city should have been told earlier "so it could go into its defensive mode."
Kelly, citing the interrogations, said the Tsarnaev brothers "planned to travel to Manhattan to detonate their remaining explosives in Times Square" four days after the Boston bombing.
A day earlier, Kelly said that Dzhokhar Tsarnaev had talked about coming to New York "to party" after the attack and that there wasn't evidence of a plot against the city. But Kelly said a later interview with the suspect turned up the information.
Kelly said there was no evidence New York was still a target. But in a show of force, police cruisers with blinking red lights were lined up in the middle of Times Square on Thursday afternoon, and uniformed officers stood shoulder to shoulder.
Outside Penn Station, Wayne Harris, a schoolteacher from Queens, said: "We don't know when a terrorist attack will happen next in New York, but it will happen. It didn't happen this time, by the grace of God. God protected us this time."
In 2010, Times Square was targeted with a car bomb that never went off. Pakistani immigrant Faisal Shahzad had planted a bomb in an SUV, but street vendors noticed smoke and it was disabled. Shahzad was arrested as he tried to leave the country and was sentenced to life in prison.
Meanwhile, the Tsarnaev brothers' father said he is leaving Russia for the U.S. in the next day or two, but their mother said she was still thinking it over.