Times Square 2 by JLaz 3
Times Square, New York City, 2013. IBTimes/Joseph Lazzaro

Update 2:15 p.m.: Dzhokhar Tsarnaev was interviewed twice and gave the information about the potential Times Square plot during the second interrogation, New York City Police Commissioner Ray Kelly told a news conference Thursday afternoon.

Kelly said Tsarnaev was interrogated in one instance from Saturday night into Sunday morning and again from Sunday evening into Monday morning.

"The information we received was that he was a lot more lucid and gave much more detailed information in the second questioning period," the police commissioner said.

"We don't know if we would have been able to stop the Boston terrorists," New York City Mayor Michael Bloomberg said. "We're thankful we don't have to find that out."

While Tsarnaev wasn't as forthcoming about the plot in his initial interview with interrogators, both Kelly and Bloomberg said authorities were working on the assumption that the suspect was not giving false information.

"We don't make light of anything," Bloomberg said. "We have to assume the worst."

The mayor said, despite the alleged plot, New Yorkers should not be concerned about their safety.

Original post: Dzhokhar Tsarnaev reportedly told investigators that he and his brother, Tamerlan Tsarnaev, planned to detonate their remaining pressure cooker bombs in an attack on Times Square three days after they exploded two of the devices at the finish line of the Boston Marathon on April 15.

The revelation of a possible second attack came on Thursday, a day after Kelly said he was told that the bombing suspects planned on visiting the Big Apple “to party,” not to use more bombs.

Dzhokhar, 19, and Tamerlan, 26, discussed an attack on Times Square that officials said was “undeveloped” and “aspirational at best,” sources told NBC News. The alleged plot was reportedly to be carried out last Thursday. Tamerlan ended up being killed in a shootout with police in Watertown, Mass., that night.

Dzhokhar, the surviving brother, elaborated about the plans after initially telling an elite team of interrogators that he and Tamerlan were thinking of visiting New York City only "to party."

After the elder Tsarnaev was killed, Dzhokhar fled and eluded capture for most of the day before FBI and other law enforcement agencies found him hiding in a boat in the backyard of a home in Watertown.

He was arraigned earlier this week on two terrorism-related charges for his alleged role in the Boston Marathon bombings.

The Obama administration made the decision not to Mirandize the 19-year-old suspect by using the “public safety” exception, which led to debate as to whether the strategy was appropriate. The Associated Press reported Dzhokhar was being cooperative with investigators before being notified of his right to remain silent but stopped talking after a judge read him his rights.

The bombings killed three people and wounded more 282 others. A fourth victim, MIT police office Sean Collier, was allegedly killed by the Tsarnaevs last Thursday, when the FBI released photos of the suspects.

The death of the officer was followed by a carjacking and a firefight, where more pressure cooker bombs were discovered in the aftermath of the incident. A manhunt for Dzhokhar ensued, causing much of the Boston metropolitan area to be told to “shelter in place.”

Dzhokhar is being kept under close guard at Beth Israel Deaconess Medical Center in Boston, where he is listed in fair condition. His medical condition was upgraded Tuesday from serious.