Kinsler, out since May 18 with a fractured rib, is targeting his return to the lineup for next week, maybe toward the end of the Rangers' 11-game homestand that started Monday.
"I'm going to see how it reacts and make sure," Kinsler said. "No setbacks."
Rangers manager Ron Washington said his hope is that Kinsler can go through the same regiment as he did Monday, which also included swinging off a tee for the second straight day.
"We wanted to give him every chance to and every movement that would maybe aggravate that area," Washington said. "He went through it really smoothly and got it done. Tomorrow we'll continue to ramp it up if he's ready."
Washington's said that depending on Kinsler's progress, he'll know in three or four days what the timetable might look like for the return of his leadoff hitter. Kinsler will go on a short rehab assignment before being activated.
Moreland pleased with progress: First baseman Mitch Moreland, out with a strained right hamstring, is optimistic he will return when his 15-day disabled list stint is up June 21.
Moreland said he ran at about 60 percent. He also did core exercises, working in particular on his lower back.
"I'm progressing like it will be 15 days," Moreland said. "I'm pretty quick to be doing that."
He said he was going to try and hit in the cages before Monday's game.
Wolf to be held back: Long reliever Ross Wolf, who gave the Rangers' a heroic effort in Saturday's 18-inning loss, will be held back Monday and Tuesday before he's available to pitch again.
Wolf went 6 2/3 innings before Toronto broke through against him for the win. Still, the journeyman pitcher, who last pitched in the big leagues in 2010, made another big impression on his manager.
"He gave 6 2/3 innings of an opportunity to win," Washington said.
Lewis update: Right-hander Colby Lewis played catch Monday and said he could throw a bullpen next week.
Lewis, who has been dealing with right elbow soreness, said this is the best he's felt since leaving Arizona for a rehab assignment a month ago.
Rangers and rookies: The Rangers have a major-league leading 23 starts by rookies, two more than any other club. The Los Angeles Dodgers, Milwaukee and St. Louis all have 21 starts by rookies.