The shootout happened Monday in Linden, New Jersey, a local and federal law enforcement official said.
Two officers were hit during the shootout with Rahami, said Chris Bollwage, the mayor of the nearby city of Elizabeth. One officer's vest was struck, and the other was shot in the hand. Rahami was shot and wounded. He was taken into custody and placed in an ambulance with what appeared to be at least one wound on his upper right arm.
Bombings in New York and New Jersey over the weekend -- as well as the discovery of several unexploded devices -- have led authorities to believe there may be a terror cell at work in those two states, law enforcement officials told CNN Monday.
And a manhunt is under way for 28-year-old Ahmad Khan Rahami after New York police identified him as wanted in connection with the bombing Saturday night in New York's Chelsea neighborhood, which wounded 29 people.
Earlier Saturday, a garbage can exploded near the starting line of a Marine Corps charity run in Seaside Park, New Jersey.
Rahami is also wanted for questioning in connection with the explosion Saturday in Seaside Park, New Jersey, the FBI said Monday.
On Sunday night, a backpack with multiple bombs inside was found in Elizabeth, New Jersey. As authorities tried to investigate, one of those bombs exploded.
The series of attacks come as New York hosts world leaders at the United Nations General Assembly this week.
Here are the latest developments:
-- Officials want to question Ahmad Khan Rahami because they believe he is the man seen in surveillance videos rolling a duffel bag near the scene of the bombing in New York's Chelsea neighborhood, according to multiple officials.
-- The FBI described Rahami as a U.S. citizen of Afghan descent with a last known address in Elizabeth, New Jersey -- the same city where an explosives-laden backback was found Sunday night.
Rahami is about 5 feet, 6 inches tall and weighs about 200 pounds. Rahami has brown hair, brown eyes and brown facial hair.
-- New York Gov. Andrew Cuomo said Monday the bombs found over the weekend have similarities, suggesting "there might have been a common linkage." He said the investigation is ongoing, and he "wouldn't be surprised if it zeroes in on a particular individual, today even," and he "wouldn't be surprised if we found a foreign connection to the act."
-- A federal law enforcement official said BBs and ball bearings were among the pieces of metal that appeared to be packed into two pressure cooker bombs in New York. One of those devices exploded on 23rd Street, but the fact that it was partly under a metal trash container may have diminished the force of the blast.
-- Surveillance videos showed the same man near the site of the explosion in Chelsea and where a pressure-cooker device was found four blocks away, several local and federal law enforcement sources told CNN.
-- On Sunday night, the FBI and New York police stopped a vehicle of interest in the investigation, according to a statement from the FBI. No one has been charged with any crime and the investigation is ongoing, the statement said.
The latest bomb discovery
The backpack in Elizabeth, New Jersey, was found around 9:30 p.m. Sunday in a wastebasket outside a neighborhood pub -- about 500 feet from a train trestle, officials said.
It contained up to five devices, Elizabeth Mayor Chris Bollwage said. The two men who found the backpack thought it might contain something valuable, but they alerted police when they saw wires and a pipe on the devices, the mayor said.
Bomb technicians sent a robot to examine the devices. As the robot was doing so, one of the devices detonated.
"The robot that went in to disarm it, cut a wire and it exploded," Bollwage said.
The remaining four devices in the backpack will be transferred in protective cases to a local site and then will be taken to the FBI laboratory at Quantico, Virginia, Bollwage said.
Police checked all garbage cans in the immediate area, but found no other suspicious items.
Police continued to search Linden and Elmora streets, close to where the backpack was found, on Monday morning. The search was connected to the ongoing terror investigation, a law enforcement source said.
Trains resumed Monday morning after the New Jersey Transit suspended service going through Elizabeth station on Sunday night. Elizabeth is about 16 miles southwest of New York City. Both New Jersey Transit and Amtrak warned of delays following the incident.
The bombing in New York's Chelsea neighborhood
Saturday's explosion shook New York City's Chelsea neighborhood and sent panicked people scrambling for cover. By Sunday, 26 of the injured who had been admitted to hospitals had been released.
A few blocks away from the blast site and shortly after the explosion occurred, investigators found a pressure cooker on 27th street with dark-colored wiring sticking out, connected by silver duct tape to what appeared to be a cell phone, officials said.
Surveillance video shows a man dragging what appears to be a duffel bag with wheels near the site of the West 23rd street explosion about 40 minutes before the blast, according to multiple local and federal law enforcement sources.
About 10 minutes later, surveillance video shows the same man with what appears to be the same duffel bag on West 27th street, multiple law enforcement sources said.
In the video, the man leaves the duffel bag where police later found the unexploded pressure cooker. After he leaves, the video shows two other men removing a white garbage bag believed to contain the pressure cooker from the duffel bag and leaving it on the sidewalk, according to a senior law enforcement official and another source familiar with the video.
Investigators have not determined if those two men are connected to the man with the duffel bag on both streets, the sources said.
The device was transported to the NYPD Bomb Squad facility at Rodman's Neck Range in the Bronx.
NYPD and FBI Bomb technicians rendered the device safe. A forensic examination of the device and its components will be conducted at the FBI Laboratory at Quantico, Virginia.
Shortly before 9 p.m. Sunday, the FBI and New York police stopped a vehicle of interest in the investigation, according to a statement from FBI. No one has been charged with any crime and the investigation is ongoing, the statement said.
3 attacks on US soil
The New York City blast occurred on the same day an explosion went off near a Marine Corps charity run in New Jersey and a man stabbed nine people at a Minnesota mall.
The Department of Homeland Security is actively monitoring and participating in the investigations in New York and New Jersey. Investigators found similarities between the explosives used in both states, according to multiple law enforcement officials, but authorities said they have not concluded the incidents are linked.
"We do not have any specific evidence of a connection, but that will continue to be considered," New York City Mayor Bill de Blasio said. "We're not taking any options off the table."
'New York is up and running'
New Yorkers will see an increased police presence around the city, de Blasio said.
Stepped-up security across the city is common as world leaders arrive for the UN General Assembly meeting, which is under way.
"You should know you will see a very substantial NYPD presence this week -- bigger than ever," de Blasio said.
Gov. Cuomo added that 1,000 additional New York State Police officers and National Guard troops will be deployed to patrol bus terminals, airports and subway stations.
"I want New Yorkers to be confident when they go back to work on Monday that New York is up and running and we're doing everything that we need to do," he said.