ST. PETERSBURG, Fla. — Nestor Cortes feels he’s ready to get back into the Yankees’ rotation.

The left-hander, on the 15-day injured list with a strained groin, threw live batting practice for the first time since the injury on Saturday. He said he was encouraged by how he felt and believes he’ll be able to rejoin the rotation during the upcoming series against the Twins in The Bronx after throwing another bullpen session Monday or Tuesday.

“It was great,’’ Cortes said after his three-inning, 45-pitch outing against minor leaguers at the Yankees’ Player Development complex in Tampa. “It went as I expected.”

After pitching in front of manager Aaron Boone, pitching coach Matt Blake and bullpen coach Mike Harkey, Cortes said there was no discomfort on any of the pitches — including a handful of sidearm pitches, which he threw to make sure those don’t cause an issue.

“That tests my groin more, when I drop down,’’ Cortes said before the Yankees’ 2-1 loss to the Rays.

He also fielded some bunts and said the injury wasn’t a concern.

Cortes noted that he got his velocity up to 92-94 mph on some pitches, which is where he wants to be during games.

“I never stopped throwing [while on the IL] so I don’t really have to build myself back up,” Cortes said.

Boone said Cortes “looked good; looked healthy.”

Luis Severino also is doing well after making his first rehab start, in his comeback from a strained lat, on Friday for Low-A Tampa.

He so far has had no problems and the Yankees have an eye on activating him when he’s eligible to come off the 60-day IL on Sept. 12.

Severino will first make another rehab start, with either Triple-A Scranton/Wilkes-Barre or Double-A Somerset, this time throwing around 50 pitches. He will perhaps then make one more, unless the Yankees decide to have him rejoin the team and make an abbreviated start with them.

The impending return of both Cortes and Severino — as well as the expectation that Jameson Taillon won’t miss a start after he was hit with a liner on his right forearm Tuesday in his most recent outing — provided some rare good news for a Yankees team that has staggered into September. Their once overwhelming lead of 15 ½ games was cut to five heading into their game Saturday against the Rays at Tropicana Field.

While the presence of both Cortes and Severino would no doubt provide a boost, the Yankees’ major issue has been a lack of offense.

Domingo German, who has filled in for Severino, has been especially effective, including Friday night in a loss to the Rays.

Oswald Peraza made his first MLB start and made a good play — showing off a strong arm — on an inning-ending double play to end the seventh. He went 0-for-3 and is still looking for his first hit in the majors.

Zack Britton’s rehab outing on Saturday went considerably better than his previous game, when he suffered leg cramps. Pitching again with Low-A Tampa as he tries to return from UCL surgery before the end of the season, the left-hander struck out two and didn’t walk any batters in a scoreless inning, during which he topped out at 92 mph.

The bullpen, also awaiting the return of Scott Effross (shoulder), Miguel Castro (shoulder), Albert Abreu (elbow) and Aroldis Chapman (leg), got a new arm on Saturday when Ryan Weber, scheduled to start with SWB on Saturday, was instead recalled. He took the roster spot of right-hander Anthony Banda, who was designated for assignment.

Banda, signed when the Yankees were in Oakland, allowed three runs in two-thirds of an inning in two appearances.

Weber pitched well in his previous stint with the Yankees this season, giving up just one run over 7 ²/₃ innings in three games.

Right-hander Stephen Ridings (back) and lefty Chasen Shreve, recently signed to a minor league deal, also faced hitters at the Player Development complex.