Alderson said the move to 13 pitchers will likely be temporary until the return of left fielder Jason Bay, who is rehabilitating an oblique injury. Bay took batting practice Sunday.
"Could be this weekend," Alderson said of Bay's return. "But right now we need the arms. In Izzy's case, it's kind of a one-way trip. It would be difficult to move him off the roster if things didn't work out. In Igarashi's case, he has options, so theoretically if we put him on the roster, we could option him out, but that is all premature at this point."
The Mets could not recall Manny Acosta since he was designated for assignment within the last 10 days. No player removed from a 25- or 40-man roster is eligible to be recalled to his Major League club unless another player is assigned to the disabled list.
"Problem No. 2 is he hasn't pitched in the time since he was designated for assignment, so he's not really ready; he's not even available," Alderson said of Acosta. "Obviously, he's there for us, continues to be there in reserve, but given the circumstances, we can't really get him back."
Isringhausen hasn't pitched in a Major League game since 2009 with the Tampa Bay Rays, but the Mets' bullpen has not impressed so far this season. Igarashi appeared in 34 games for New York last season, posting a 7.12 ERA. He has made two appearances for Triple-A Buffalo this season.
"It's been inconsistent," Alderson said of the bullpen. "Probably as positive an adjective as I can use. But it's unfortunate. It's one of those things. It's going to happen over the course of the season. Hopefully we'll get a couple of other arms in here and settle things down a little bit, and it won't be as stretched as it has been the past couple of days.
Isringhausen has battled through injuries throughout Spring Training and agreed to stay in Port St. Lucie, Fla., after the team broke camp.
"He's put in a lot of work and deserves the opportunity, and it's time for us to give him a shot."