NEW YORK — The man who planted a car bomb in Times Square boasted that he thought it would kill at least 40 people and that he planned to detonate a second bomb two weeks after the first, prosecutors said Wednesday, quoting the former financial analyst in a video where he said he’d hoped “to join my brothers in jihad” ever since the Sept. 11 attacks.

Faisal Shahzad should get life in prison when he is sentenced Oct. 5, prosecutors said in a filing, arguing that he “had every intention of delivering a powerful and terrorizing strike to the heart of New York City.”

The government noted that Shahzad showed no remorse when he pleaded guilty on June 21 after confessing to investigators.

In fact, prosecutors wrote, “he spoke with pride about what he and his coconspirators had done.”

Included in the government submission to the sentencing judge in U.S. District Court in Manhattan was a 40-minute video in which Shahzad fires a machine gun in what appears to be the mountains of Pakistan as he announces that he has met members of the Pakistan Taliban and has decided “we are going to raise an attack inside America.”

Prosecutors also included a video of the government’s explosion of a bomb the size of Shahzad’s, saying the results last June in a Pennsylvania field show the attack would have been “devastating to the surrounding area” had it succeeded.

Through most of the first video, Shahzad is seated and quoting from the Quran but makes his intentions clear toward the end when he states: “I have been trying to join my brothers in jihad ever since 9/11 happened. I am planning to wage an attack inside America,” prosecutors said.

Shahzad was arrested two days after his May 1 bomb attempt in tourist-filled Times Square, where the explosives he had packed into the back of a sports utility vehicle sputtered and failed to detonate.

Prosecutors said he tried to ignite the bomb before he abandoned the vehicle and that he was “prepared to conduct additional attacks until he was captured or killed.” The government did not list other locations that Shahzad might have chosen as targets.

The second video shows an explosion shot from various angles, sometimes in slow motion. It caused a giant fireball that ripped apart the mock car bomb and five other vehicles positioned around it to simulate traffic. It also sent debris flying into a nearby pond.

Shahzad’s lawyer did not return a request for comment Wednesday.

Shahzad chose a warm Saturday evening to carry out his attack in a part of Times Square he believed would be most crowded based on streaming video of the world-famous tourist magnet that he’d looked at online, prosecutors said.

He lit the fuse of his bomb, then left the vehicle to head to Grand Central terminal and, from there, his Connecticut home, pausing along the way to listen for the explosion that never came, the filing said.

A street vendor spotted smoke coming from the SUV and alerted police, who quickly cleared the area. The bomb attempt set off an intense investigation that culminated two days later with investigators plucking Shahzad off a Dubai-bound plane at a New York airport.

The government made clear that much of its information came from Shahzad, who waived his right not to incriminate himself.