New York State Police Superintendent Wayne Bennett said Phillips was not in custody Friday afternoon. It could not be determined if Phillips was hit by the gunfire; Bennett said there was no sign of blood at the scene.
Phillips, a career thief who broke out of an Erie County jail in April, is suspected of killing a state trooper and wounding two others.
"We believe we have him contained," Bennett said, but added, "I won't say that I'm completely convinced that this is going to come to the conclusion we want."
Bennett said a police dog caught the trail of an individual in the woods about 9 a.m. When the officer came up behind the man, he turned and pointed a pistol at the officer. The officer fired several rounds and the individual fled into another wooded area.
"We have every reason to believe it's Ralph Bucky Phillips," Bennett said.
Bennett said police believe they have Phillips contained in an area near Carroll, about 65 miles south of Buffalo.
"There wasn't really any time to put a plan into effect," Bennett said when asked if police thought Phillips managed to escape. "He hasn't had any time to make any contact with a safe house."
"Obviously we have a very dangerous and desperate individual on the loose here," he said.
Authorities swarmed a golf course Friday morning, landing on the course in a helicopter about 9:30 a.m. and using a loud speaker to clear out about 100 golfers.
Marge Bortz, owner of Cable Hollow Golf Course in Russell, Pa., eight miles from Carroll, N.Y., told The Associated Press that police informed her Phillips is in the woods around the golf course.
The course was closed and there were 10 people locked in the clubhouse, including Bortz's family and three employees.
"My son said it was like a platoon of policemen who went in the woods in camo," she said. "There's police all over the place."
The search is in a hilly, heavily wooded area cut through by creeks and dotted with seasonal camps and hunting stands.
Clifford Cable, 81, lives about a mile from the golf course and has hunted the hilly terrain for decades.
"It's woods everywhere here," he said. "You could hide anywhere."
Warren County District Attorney Ross McKeirnan said a suspect believed to be Phillips was seen running into the woods at about 2 a.m. Friday. Two cars in Warren County were reported stolen overnight, he said.
A law enforcement source familiar with the investigation told The Associated Press that items in a backpack recovered from one of the stolen vehicles led police to believe Phillips was back on the prowl.
The source, who spoke on condition of anonymity because he was not authorized to talk about the case, said Phillips apparently stole a car out of a driveway in Carroll. The owner heard it and called police, sparking the search.
Phillips, 44, became the subject of a massive search after allegedly shooting a state trooper near Elmira in June. The trooper survived.
The 6-foot-tall, 240-pound Phillips, who has threatened "suicide by cop" and once promised to "to splatter pig meat all over Chautauqua County," is on the FBI's 10 Most Wanted Fugitives list, the federal marshals' 15 Most Wanted list and was to be featured on "America's Most Wanted."
Authorities believe Phillips has been helped by numerous people since his escape, but has also broken into unoccupied hunting cabins in New York and Pennsylvania and stolen about 15 cars to remain ahead of police, authorities said.
Phillips may have spent 11 days hiding out in a western Pennsylvania home last month, slipping back into New York at least once to steal 41 guns from a gun shop, authorities said.
Investigators are looking into whether one of the stolen guns was used in the shootings of two New York state troopers on Aug. 31 as they staked out the home of Phillips' former girlfriend.
Trooper Joseph Longobardo died Sunday; Donald Baker Jr. has been in critical condition since the shooting. Both troopers were struck with bullets from a high-powered rifle.