The Chicago Cubs' Yu Darvish appears to be on track for a minor-league rehab start after throwing strongly in a simulated game Tuesday as the right-hander continues to work through injuries to his pitching arm.

Darvish faced two Cubs batters and threw 55 pitches over three innings, his longest simulation so far. He allowed a home run but held each batter to two hits.

"He looked totally involved," Cub's manager Joe Maddon said, according to MLB.com. "He was absolutely competing out there, that's the word I used. He got upset with himself when he spiked one fastball, which I kind of liked. He looked really good and was not holding back."

Darvish, 31, went on the disabled list on May 26 with right triceps tendinitis. He faced batters in a two-inning simulated game last Wednesday for the first time since a minor league game on June 25, after which he was diagnosed with right elbow inflammation.

The National League club has yet to decide a timetable for Darvish's return, but Cubs president of baseball operations Theo Epstein said Darvish's arm strength, endurance and intensity were encouraging.

"Today versus the one in Kansas City, for example, I think he let a few more pitches go today," Epstein said. "He was competing a little more, instead of just trying to get a feel for his stuff and throw it to certain spots. That's the point you want to get to before he goes out to a rehab situation."

In eight games this season, Darvish is 1-3 with a 4.95 ERA.