The near-fatal stabbing of a Texan tourist on a C train Tuesday afternoon was just the beginning for a man with an 8-inch folding knife, police said yesterday.

Twelve hours later, the suspect wielded his knife again – this time, stabbing a cook at a subway station in Rockefeller Center, police said. More than an hour later, he struck for the third and final time, stabbing two Canadian tourists each in the back as they walked near Times Square. He was arrested soon after.

The suspect, identified as Kenneth Alexis, 21, admitted to all four stabbings, police said. In the stabbing of the two women, police charged Mr. Alexis with two counts of assault, two counts of criminal possession of a weapon, and possession of marijuana. For the C train stabbing, he was charged with attempted murder in the second degree and criminal possession of a weapon in the fourth degree. Charges in the other incidents were pending last night. His last known address is a homeless shelter in Midtown, the Safe Horizons Streetwork Project, police said.

Police said he had been arrested in the city in the past for attempted assault and harassment. In his hometown of Boston he has a record of criminal trespassing, shoplifting, and criminal mischief.

The police commissioner, Raymond Kelly, called the spate of stabbings a disturbing but uncommon series of events. Subway crime is down 26.7% in 2006 compared to the same period last year, CompStat reports show.

“I can understand people being apprehensive, but the subways are cleaner, safer than ever before,” he said.

The first stabbing occurred at about 3:30 p.m. on Tuesday, just as the southbound C train that Christopher McCarthy, 21, and his girlfriend were riding in pulled into 110th Street station. A man, dressed all in black with a black baseball cap, came forward and punched Mr. McCarthy in the chest before exiting into the station, witnesses said.

It was only when the doors shut and the train started moving again that Mr. McCarthy realized he had been stabbed once in the heart, police said. Passengers notified the conductor, who called the authorities. He was rushed to St. Luke’s hospital, where he is in a critical but improving condition.

The couple was visiting New York from Houston, Texas, and staying in Connecticut. Mr. McCarthy’s family flew in to be at his bedside yesterday. At a brief but emotional press conference, Mr. McCarthy’s father, Joseph McCarthy, said his son was not bitter about the unmotivated attack.

“My son has forgiven his attacker,” he said.

Mr. Alexis allegedly fled the station into Central Park. More than 12 hours later, at 3 a.m., he resurfaced at Rockefeller Center Subway station at 50th Street. He approached two men on a southbound F train platform, and demanded that Ambrosio Castro, 30, give him his cell phone. Mr. Castro and his companion, Jorge Martinez, 35, were returning to Brooklyn from the Japanese restaurant where they work on 49th Street.

Mr. Castro didn’t understand what Mr. Alexis was saying, but said “no,” Mr. Martinez said.

“Then he stabbed him,” Mr. Martinez said through an interpreter. Mr. Castro was able to make it to the token booth, where a station attendant called the authorities. He was taken to St. Vincent’s Hospital, where he was listed in stable condition yesterday. He has stab wounds in his abdomen and chest.

At 3:30 a.m., Mr. Alexis showed up at a delicatessen near Columbus Circle called West Park Market, police said. He drank a bottle of water without paying and tried to leave with several beers. When the store clerk tried to stop him, he threw a bottle of beer on the floor and fled south, police said.

He was next sighted across from the W Hotel on 47th Street by a group of cab drivers. One driver, Samuel Dupiton, 45, said Mr. Alexis came up to him and shook his hand, mumbling that he was from New Jersey.

“He was acting strange,” Mr. Dupiton said.

Meanwhile, a group of women arrived half a block west on the street at the Edison Hotel, where they were staying. One of the women asked a bell hop where she could find a fast food restaurant in the area and he directed her and another girl, identified by police as Melanie Carrier, 22, and Audrey Perrier, 25, to walk east toward McDonald’s on 7th Avenue. The women, who hail from Toronto, Canada, are in the city for a week-long vacation.

Mr. Dupiton said Mr. Alexis crossed the street and approached the women, trying to put his arm around the waist of one of them. When they told him to leave, he followed them. As they crossed the street into Duffy Square, he came up from behind and swung his knife like a pendulum into each woman’s lower back once.

“It looked like he was going to take their pocket books,” another of the cab drivers, Andrew Fequiere, 69, said. “One girl fell down. We wondered what happened.”

The women made it back to the front of the W Hotel, where a security guard called paramedics. Several of the taxi drivers and a security guard followed Mr. Alexis to the McDonald’s on 7th Avenue, making 911 calls about the attacks along the way.

As police surrounded the restaurant, Mr. Dupiton and the others watched Mr. Alexis try to blend in with other customers and get away.

“I yelled, ‘That’s the guy. Lock him up. Lock him up.’ ” Mr. Dupiton said.

Ms. Carrier and Ms. Perrier were taken to St. Vincent’s hospital, where they were listed in stable condition.

Mr. Alexis was expected to be arraigned in Manhattan early this morning.