Speaking through translator Tomas Vera, Iglesias said he felt good while throwing 30-35 pitches.
"I haven't had any discomfort or anything, thanks to the doctors, thanks to the trainers -- I feel really pleased where they were for me today," Iglesias said.
Reds manager Bryan Price expected Iglesias to get two more bullpen sessions before he would be cleared to begin a Minor League rehab assignment.
"He hasn't had any issues with the oblique since he started his throwing program last week at home, so moving forward, as long as he doesn't have any problems, I could see him getting close to being ready to throwing in a Minor League game here in the next several days," Price said.
Iglesias was optimistic he could be ready to return to the Reds' rotation in early-to-mid July.
"I feel confident in my abilities that I'll be ready to be part of the team again before the All-Star Game," Iglesias said.
• 2015 Draft: Signing and Bonus Tracker
• The Reds announced Wednesday that they have signed two more 2015 Draft picks. They were fifth-rounder Ian Kahaloa, a right-handed high school pitcher from Hawaii, and Alexis Diaz, another high school right-hander from Puerto Rico who was taken in the 12th round. Cincinnati has signed 16 of its top 17 Draft selections and 20 of 41 picks overall.
Mark Sheldon is a reporter for MLB.com. Read his blog, Mark My Word, follow him on Twitter @m_sheldon and Facebook and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.