SCOTTSDALE, Ariz. —  Baseball Commissioner Bud Selig wants tougher penalties for major league players who violate the sport's drug agreement.

Players' association head Michael Weiner said the union is willing to discuss changes, but only ones that would start in 2014.

Speaking at a news conference Saturday, Selig said the situation surrounding last year's positive drug test of All-Star game MVP Melky Cabrera and allegations players received banned substances from a now-closed Florida anti-aging clinic helped lead him to seek stiffening of penalties as quickly as possible.

He declined to give any specifics of what he had in mind, saying MLB Executive Vice President Rob Manfred and Weiner will meet. Selig said he wants increased penalties "as expeditiously as possible."

Weiner said Monday that some players have expressed support for tougher penalties. Selig said he was encouraged by Weiner's comments.

"The players have been discussing whether changes in the penalties are warranted since the offseason," Weiner said during a telephone interview Saturday. "As I've said throughout spring training, there's a variety of player views on this subject. In fact, during the offseason we suggested to the commissioner's office the possibility of differential penalties namely advanced penalties for certain intentional violations but reduced penalties for negligent violations.

"That format was not of interest to MLB at that time. We look forward to ongoing negotiations over the drug program, but any change in the penalties would be a 2014 issue. It would be unfair to change the drug-testing rules now that the 2013 program has begun to be implemented."

MLB and the union started urine testing with an anonymous survey in 2003 and added penalties in 2004, when a first offense resulted in counseling. A 10-day suspension for a first offense was added for 2005 and the current discipline structure has been in place since the 2006: 50 games for an initial steroids infraction,100 games for a second and a lifetime ban for a third. No player has reached the third level.

The initial penalty for a stimulants offense is counseling, with a 25-game penalty for a second violation.

Twelve players were given 10-day suspensions in 2005. Thirty suspensions have been announced from 2006 on, including just two 100-game bans — to pitcher Guillermo Mota and catcher Eliezer Alfonzo. The penalty for Alfonzo was cut to 48 games because of procedural issues similar to the ones that led an arbitrator last year to overturn Ryan Braun's positive drug test before a suspension was announced.

Positive tests increased to eight last year, when Cabrera, Bartolo Colon and Yasmani Grandal all tested positive for testosterone.

"We've made meaningful adjustments to our testing and the time has come to make meaningful adjustments to our penalties," Selig said.

Selig announced after a January owners' meeting that management and the union agreed players will be subject to blood testing for human growth hormone during the regular season and that the World Anti-Doping Agency laboratory in Laval, Quebec, will keep records of each player, including his baseline ratio of testosterone to epitestosterone. The lab will conduct Carbon Isotope Ratio Mass Spectrometry (IRMS) tests of any urine specimens that "vary materially."

With spring training blood sampling that started in 2012, MLB became the first major sports league in North America to test for HGH.

"There is no question that there have been enough events that say to me the program is good but apparently the penalties haven't deterred some people," Selig said.

He said that those who have flaunted the anti-drug rules are "a very small percentage" of players.

"A great majority really, really have been terrific," Selig said, "and I give the players association a lot of credit. We had lots of problems two decades ago, 10 years ago, but I'm confident that Michael and Rob will sit down because I feel very strongly about this."

Cabrera, who was leading the NL in hitting and was the All-Star MVP while playing for San Francisco, was suspended for 50 games for testing positive for elevated levels of testosterone. He signed a two-year, $16 million contract with Toronto in the offseason.

Selig would not comment on the now defunct Biogenesis of America clinic in Coral Gables, Fla., other than to say it is the subject of a "very thorough investigation" by MLB.

The facility was alleged in media reports to have provided performance-enhancing substances to several players, including Cabrera, Alex Rodriguez and Nelson Cruz. The players have denied they got banned drugs from the clinic.