Mulder is working his way back after undergoing shoulder surgery in each of the past two seasons.
"I would say it's going in the direction it's supposed to be going," Cardinals general manager John Mozeliak said. "He feels good. But he still has room for improvement."
Mulder threw six innings for Double-A Springfield on Sunday, allowing three hits, three walks and no runs while striking out one. Two of Mulder's three walks came in his final inning. His fastball, according to Mozeliak, averaged 87 mph, an upgrade from his previous start, when he started at 85-87 and dropped to 83-85.
"I think they felt like he got a little tired in the sixth, which was apparent from the walks," Mozeliak said. "But from a medical standpoint and a results standpoint, it was positive."
St. Louis manager Tony La Russa said he received positive reports on Mulder's outing, but believes the pitcher should wait as long as possible before taking the mound in big league games.
"He needs to come up not in a process of rehabbing, but ready to pitch," La Russa said. "Ready to pitch like Mark Mulder -- to the best of his ability. That's what we want to have happen. He could take 10 more starts -- whatever it takes. There's potentially too much good there."
Mulder's next start will come on Friday for Springfield at Tulsa.
Matthew Leach is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.