Souza suffered a left hip strain on Wednesday while sliding into second base.
"He looked really good running [at Tropicana Field on Friday afternoon]," Rays manager Kevin Cash said. "So that's good news. We were optimistic that it wasn't too bad."
Souza made a pinch-hit appearance in the 10th inning of the Rays' 4-3 loss, singling to left before being retired on a double-play grounder.
Kevin Kiermaier (right hip fracture) is making progress, as well. The Rays' center fielder went on the disabled list on June 9 and is eligible to be activated on Aug. 9.
"I've been pretty much pain-free the whole time, and the progression has been smooth and steady," Kiermaier said. "And all baseball activities that I've done to this point, I couldn't be happier about. So very happy about how everything is going. So I hope for another great two weeks and then be back on the field as soon as I can."
Infielder Daniel Robertson (neck spasms) is back to taking part in baseball activity, noting that his neck pain is now gone. Robertson has been on the 10-day DL since June 27.
"I think [Kiermaier] and [Robertson] both will be with us for a couple of days then we'll start talking about getting them out on a rehab assignment," Cash said.
Right-hander Matt Andriese (right hip stress reaction) threw off a mound on Friday for the first time since going on the 60-day DL on June 13 (retroactive to June 11). Once he's up to speed, he will need to be stretched out as a starter before returning to the rotation.
Matt Duffy (recovery from Achilles surgery) has been hitting and throwing while working to build up strength in his leg before he starts running again. The Rays' shortstop doesn't like speculating about when he might return, but he allowed that they "should have a solid idea" about his return by the middle of August.
• Right-hander Jumbo Diaz, who was designated for assignment on Monday, has cleared waivers and has elected free agency. And the Rays have released right-hander Danny Farquhar from Triple-A Durham. He hasn't been on the 40-man roster since the Rays DFA'd him on 29.
• The Rays have have awarded a total of $100,000 to 20 local nonprofit organizations through the Rays Baseball Foundation Community Fund Grant Program. Each recipient was recognized in a pregame ceremony prior to Friday's Rays-Rangers game.
• The Rays Community Fund Grant Program provides assistance to local nonprofits in the Tampa Bay region. The $5,000 grant is awarded to help support and enhance current programs offered by community-based nonprofit organizations. To date, the Community Fund Grant Program has awarded more than 296 grants to local charities totaling more than $1.5 million.
Bill Chastain has covered the Rays for MLB.com since 2005.