Francisco (1-2) has blown saves in his two opportunites this season, both leading to Rangers losses, and has a 27.00 ERA in three appearances.
Feliz, whose fastball is regularly clocked in the high 90s, has been the eighth-inning setup man, striking out five in 2 1/3 innings over three games.
"He's our closer until I get Frankie back there," Rangers manager Ron Washington said before Sunday's series finale against Seattle. "Frankie will be the closer of the Texas Rangers. We're just giving him a chance to get himself together."
Francisco's fastball has dipped from the mid-90s last season to the low-90s, and many of his pitches have been over the middle of the plate.
"He's not the animal, the guy we've seen come in and make people understand that this game is over," Washington said. "We haven't seen that guy. His location has been off and he hasn't had a chance to use all his pitches. We just want to give him a break."
On Saturday, Washington was noncommittal when he was asked if Francisco had lost his job after he gave up three runs and three hits while registering only one out as Seattle rallied in the ninth for a 4-3 victory.
But Washington and pitching coach Mike Maddux later decided to make a change, meeting with Francisco before Sunday's game.
Last season Francisco converted 25 of 29 save opportunities with a 3.83 ERA. But he spent three stints on the disabled list, two with right arm problems.
Washington said Francisco's problems aren't physical.
"To me, he's fine," Washington said. "Frankie's a very intelligent guy. He says he's healthy. He just hasn't gotten the job done. We need to give him time to get it right."
Washington said several times that the situation was only temporary, that he expects Francisco to reassume the end-of-game role at some point.
"There's no way we can see ourselves making it through this year without Frankie Francisco being who he is," Washington said.
For now, Francisco will continue to pitch out of the bullpen, but in a "less stressful situation" that was unspecified by Washington.
Washington said Francisco can still be effective without a dominant fastball.
"I've seen guys go out there at 92, 93 and get outs," Washington said. "Frankie can get people out at 92, 93. I know we're used to seeing 95, 96, and we expect that to come back. But he has enough to get outs. He's just not putting the ball where he wants to."
Francisco has admitted he has been "missing a lot in the middle" of the plate and now must deal with the fallout.
The concerns over Feliz are his lack of experience and the fact that the Rangers have been protective of his arm.
Washington said pitch count would determine whether Feliz will close in consecutive games.
"A lot will depend on how he uses his pitches," Washington said. "If he goes out there and throws 28 pitches, of course we've got to go in another direction. But if Frankie's closing and throws 20-something pitches, we would do the same thing. It's tied to what it takes for him to get three outs."