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04/19/2013 8:07 PM ET

Teixeira increasing rehab activity, but Yanks cautious

TORONTO -- Mark Teixeira, who is recovering from a partially torn tendon in his right wrist, is slowly making strides on his road to recovery.

The first baseman has started taking swings with a light fungo bat, shortly after he incorporated underwater swings in a pool, as he ramps up his rehabilitation process.

Manager Joe Girardi said Teixeira must still exercise caution.

"I think a lot of times these guys think when they come off a brace, and I can tell you I did, too, that they can swing because it feels good," Girardi said.

"It just takes time, that's all."

Girardi said recovering players can be deceived by how good they feel once they start incorporating certain exercises. But he added that swinging a properly weighted bat at the force required in a game situation takes a much different kind of strength.

Meanwhile, the skipper didn't have any new information to pass along regarding Teixeira's fellow injured teammate, Curtis Granderson, but thinks his tremendous shape will help expedite the rehab process once he's cleared to resume baseball activities.

"I don't know that he has to go through a full Spring Training," Girardi said. "We really won't be able to determine how much he needs until he goes and plays some games, because you don't know how his body is going to respond and how he feels in the game."

Granderson and Teixeira combined to hit 67 of New York's Major League-leading 245 home runs last season. The Yankees entered play Friday first in the American League with 22 homers.

Rivera can empathize with Jeter's plight

TORONTO -- If anyone can relate to what Derek Jeter is going through, it's teammate Mariano Rivera.

After Jeter's latest setback, the discovery of a new fracture in his surgically repaired left ankle that is expected to keep him out until after the All-Star break, the shortstop is likely to play in his fewest games since the 1995 season, when he appeared in 15 contests.

A torn ACL forced Rivera to miss the majority of the 2012 season, and he said it wasn't easy not being able to compete and be around his teammates.

Rivera believes the best thing Jeter can do is take care of himself and not rush a return to the field.

"He has to be selfish and think about himself for once," Rivera said. "Think about what you have to do to get ready. Forget about what I can do for the team, he can't do [anything] for the team right now. What he can do for the team is make sure [he is] 100 percent mentally and physically, and then you are ready to help the team."

Rivera said he spoke to Jeter about two weeks ago to check in on him, and the captain told him things were going well. He hasn't talked to Jeter since the latest incident, but he is hoping to get in touch with him soon.

Manager Joe Girardi reached out to Jeter on Friday but didn't have any luck getting through. Girardi wanted to stress that Jeter was cleared to play at the beginning of March, so he wasn't rushed back, and that he doesn't think this latest setback will finish him.

In fact, Girardi believes the 38-year-old still has plenty of good baseball left in him.

"I really believe that, when he's healed, he's going to be a good player for us," the skipper said. "It's just a matter of when, is what we have to deal with. I think once he heals up and we get him back, he'll play at a high level. But the question now is, when is it going to be?"

The last game Jeter played was Game 1 of last season's American League Championship Series, during which he was forced to exit in the 12th inning after fracturing his ankle on a play at short. The Yankees' closer said that is not a lasting image Jeter wants people to have.

"Knowing him, that's the last thing he would want people to remember," Rivera said. "As a player, and the type of player that he is, sometimes we push a little bit farther than we need to push. But that's our nature."

What Rivera misses most about Jeter, besides his ability to help the club win, is his presence in the clubhouse. The Yankees, Rivera said, are missing their captain, one who leads by example.

"He doesn't need to say much," Rivera said about Jeter's leadership qualities. "He will say something when he needs to say it, but most of the time it's by example. Being there, playing hard, respecting the game, be there for your teammates, all that -- that's what is missed."

Jeter is one of many Yankees stars who have yet to play this season, a list that also features Curtis Granderson, Mark Teixeira and Alex Rodriguez. But Rivera said that's no excuse for New York not to compete.

"We can't sit and wait for Derek and the others to come back," he said. "We still have to do the job that we need to do.

"We will be praying and hoping that he recovers soon."

Chris Toman is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.