ST. PETERSBURG, Fla. (AP) – Injured Red Sox pitcher John Smoltz could resume throwing Wednesday or Thursday.

Smoltz, recovering from shoulder surgery last June, is currently taking part in a one-week workout program to build strength.

“I work hard, and I’m working smart,” Smoltz said before the Red Sox played the Tampa Bay Rays on Saturday night.

Smoltz has been working out with Boston’s extended spring training team, and threw in a simulated game before being shut down.

“He actually feels pretty good,” Boston manager Terry Francona said. “I think he has days, probably, where he’s frustrated because he wants to be pitching. That’s why he’s still pitching.”

Smoltz, with 210 career victories, agreed to a $5.5 million, one-year deal with the Red Sox in January after 20 seasons with the Atlanta Braves. The 41-year-old right-hander might be ready to pitch in the majors next month.

“June is very realistic,” Smoltz said.

Also, Daisuke Matsuzaka, out with a mild right shoulder strain, threw a bullpen session and will pitch for Triple-A Pawtucket on Tuesday. He will throw three innings or around 45 pitches in the first of what could be several outings in the minors.

Mark Kotsay, rehabbing after back surgery, was the designated hitter Saturday for Pawtucket. He is expected to play in the outfield Sunday.

Outfielder Rocco Baldelli, sidelined by a strained left hamstring, is set to join Pawtucket on Monday.