Bassitt, however, could be summoned again should Cahill land on the disabled list. Athletics manager Bob Melvin said the veteran right-hander was "a little better" Sunday, but didn't rule out a DL stint.
Smolinski returns to the A's a second time this season, after hitting .118 with 34 at-bats during his first stint. He was optioned to Nashville on May 16 and slugged seven homers in 21 games with the Sounds, batting .260.
He launched five of those homers in his last nine games, hitting .355 in that span.
"He's doing well," Melvin said. "He's the kind of guy when you get consistent at-bats you've got a much better chance. The trick here is trying to stay ready, especially for younger guys. It's an acquired taste to be a guy that doesn't play every day."
• Right-hander Andrew Triggs (triceps) threw a bullpen session Sunday and is nearing a Minor League rehab assignment.
• Outfielder Boog Powell, who has been sidelined since April 7 with a sprained right knee, was back in action Saturday, making his first rehab appearance for Class-A Advanced Stockton.
Powell, who was hitless in three at-bats and played five innings in center field, is slated for seven more innings with Stockton on Monday and said he expects to transfer his rehab to Nashville by the end of the week.
Jane Lee has covered the A's for MLB.com since 2010. Follow her on Twitter @JaneMLB.