Pitching coach Jim Hickey noted that Moore's velocity was almost at game speed and that he showed a "great curve."
"I couldn't imagine it feeling better based on how the last two weeks went," Moore said.
Moore will throw another bullpen session on Tuesday and could possibly be back in the rotation for next weekend's series against Oakland.
"That's in a perfect world, if everything goes well Tuesday and Wednesday," Moore said. "Still, [I] just [have to] continue with the same regimen as far as treatment goes. Today it was really just a great conditioning day for my shoulder, my lat, all the baseball-specific muscles. And I didn't feel like I got tired at the end of it. And it was a good workday."
Hickey noted that the training staff needs to weigh in on Moore's next move but added that a simulated game might not be necessary.
Pitching for the Rays next weekend "would not be any kind of surprise," Hickey said.