NEW YORK - At least eight players — and possibly more — on the list of 104 names seized by the government did not test positive for steroids, Major League Baseball said Saturday.

In statements ahead of a news conference at Yankee Stadium, the commissioner’s office and union general counsel Michael Weiner said the number of players on the list exceeds the number that the union and management agreed had tested positive.

“There are more names on the government list (104) than the maximum number of positives that were recorded under the 2003 program (96),” MLB said in a statement. “And, as the Mitchell Report made clear, some of the 96 positives were contested by the union. Given the uncertainties inherent in the list, we urge the press and the public to use caution in reaching conclusions based on leaks of names, particularly from sources whose identities are not revealed.”

Weiner said some positives could have been caused by nutritional supplements and that some scientific questions remain over the 2003 survey tests.

The New York Times reported last month that David Ortiz and Manny Ramirez were on the 2003 list and said earlier that Sammy Sosa was on it. Because the list is under court seal, the union said it can’t confirm or deny the report and the commissioner’s office said it doesn’t possess the government list.

“I definitely was a little bit careless,” Ortiz said Saturday. “I was buying supplements and vitamins over the counter ... but I never buy steroids or use steroids.

“I wanted to aplogize to fans for the distraction, my teammates, my manager,” Ortiz added, a few hours before the Boston Red Sox played the New York Yankees. “This past week has been a nightmare.”

Weiner said a player alleged to be on the list “finds himself in an extremely unfair position; his reputation has been threatened by a violation of the court’s orders, but respect for those orders now leaves him without access to the information that might permit him to restore his good name.”

Baseball said in November 2003 that 5 to 7 percent of the of 1,438 anonymous tests in that year’s survey were positive for banned substances, which works out to 72 to 101 tests.

“Accordingly, the presence of a player’s name on any such list does not necessarily mean that the player used a prohibited substance or that the player tested positive under our collectively bargained program,” Weiner said.

The survey was designed to determined whether baseball needed mandatory random drug testing with penalties starting in 2004, with a 5 percent threshold for positives triggering future testing. While the exact number of 2003 positives was subject to dispute, the sides never worked that out because they agreed the percentage was over the threshold.

Slideshow   The Week in Sports Pictures The Giants on top of the football world, getting ready for the London Olympics and more. more photos

“Substantial scientific questions exist as to the interpretation of some of the 2003 test results,” Weiner said. “The more definitive methods that are utilized by the lab that administers the current drug agreement were not utilized by the lab responsible for the anonymous testing program in 2003. The collective bargaining parties did not pursue definitive answers regarding these inconclusive results, since those answers were unnecessary to the administration of the 2003 program.”

Under the rules of the 2003 testing, Weiner said “legally available nutritional supplements could trigger an initial ’positive’ test under our program.”

“Each ’test’ conducted in 2003 actually consisted of a pair of collections: The first was unannounced and random, the second was approximately seven days later, with the player advised to cease taking supplements during the interim,” he said. “Under the 2003 program, a test could be initially reported as ’positive,’ but not treated as such by the bargaining parties on account of the second test.”

Also on NBCSports.com Beyond the Arc: No. 11 Mich. St. takes big step forward Chandler: Jeremy Lin was special even in 8th grade What NFC teams need this offseason  |  And AFC DeMarco: Dodgers could become a contender Follow us on Twitter: @NBCSports  |  And Facebook