Investigators have expanded to North Carolina their frantic search for a suspect in the shooting of two police officers during a traffic stop of a stolen SUV, a law enforcement official said Wednesday.

The ex-convict, Dexter Bostic, 34, has extended family in that state and police believe he may have fled there sometime after Monday’s shooting in Brooklyn to hide out, said the official, who spoke to The Associated Press on condition of anonymity because the investigation has not been completed.

With their photos on wanted posters and a $64,000 reward offered for information leading to their capture, Bostic and a second suspect, Robert J. Ellis, 34, remained at large early Wednesday, two days after the shooting that left one officer with life-threatening injuries.

Both Bostic and Ellis both are parolees with long records of violent crime, according to police. Bostic, also known as Marcus Jackson and Dexter Bostick, is a former employee of a Long Island car dealership where the BMW sport utility vehicle was stolen, police said.

Via television, Bostic’s relatives implored him to turn himself in and said their thoughts were with the officers.

“We’re praying that they have a speedy recovery, that everything will be back to normal,” the suspect’s sister, Nicole Bostic, told WCBS-TV Tuesday night. “Our prayers and our hearts are going out to their families.”

A lawyer for the Bostic family did not immediately return a telephone message requesting comment.

A third suspect, identified by police as Lee Woods, was arrested on charges of attempted murder, assault on a police officer with a deadly weapon, unauthorized use of a vehicle and other offenses.

Police said Woods, 29, was arrested Monday at the Queens home of Bostic’s sister, the mother of their child, and that he had numerous prior arrests on charges of assault, weapons possession and other crimes. As Woods was being led from a police station in handcuffs Tuesday night, he denied any wrongdoing.

“I ain’t do nothing,” he said.

One of the officers, Belarus-born Russel Timoshenko, 23, remained in “very, very grave condition” with a severe head wound, Police Commissioner Raymond Kelly said.

The second officer, Herman Yan, saved by his bullet-resistant vest, was released from the hospital Tuesday. He told WNBC-TV he was hopeful his partner would recover.

“I believe in miracles,” Mr. Yan said from the doorway of his Brooklyn home. “I will recover fully, get back on the street again. I hope the same thing happens to him.”

Mr. Yan suffered wounds to his chest and forearm. Police said it appeared that his bullet-resistant vest saved his life; Mr. Timoshenko also wore a vest.

The shooting occurred at 2:30 a.m. Monday in Brooklyn’s Crown Heights section, after the two officers used a laptop computer in their marked patrol car to do a random check of the license plates on the BMW. After discovering the plates didn’t match the car, they turned on their flashing lights and pulled the car over.

As the uniformed officers followed procedure by approaching from either side of the SUV, investigators believe, two of the occupants simultaneously opened fire without warning, hitting Mr. Timoshenko first.

A security camera from a day care center at the intersection where the shooting took place captured grainy images of the officers approaching the stolen car. It also shows Mr. Timoshenko taking fire and falling backward, then Mr. Yan getting caught in a shootout, police said.

Ballistics evidence from the scene indicated that one of the occupants of the car fired twice at Mr. Timoshenko, while another fired five times at his partner. Mr. Yan managed to get off a dozen shots before the BMW sped away, police said.

Detectives who were canvassing the area while investigating an unrelated double homicide heard the shots and stopped to help the officers. Other police cars arrived moments later and rushed the victims to the hospital.

Investigators later determined that the SUV, and the plates from the second vehicle, had been stolen from Five Towns Mitsubishi in Inwood, N.Y., on Long Island near the Queens border. Inside it were two .45-caliber shell casings and trash from a recent meal of fried chicken from a fast-food restaurant, police said.

Investigators also obtained footage from a second camera showing three men ducking into a driveway next to a building after ditching the stolen vehicle a few blocks from the shooting. The three guns were discovered behind the building.