Mets manager Carlos Mendoza said Tuesday that Butto will remain in the team's bullpen, Tim Healey of Newsday reports.
Butto (6-3) picked up the win Thursday, walking one batter in a scoreless inning of relief.
Butto gave up a run on four hits and a walk over three innings to record his second save of the season in Monday's win over the Twins. He struck out two.
The Mets recalled Butto from Triple-A Syracuse on Tuesday, Anthony DiComo of MLB.com reports.
Butto could make a spot start for the Mets prior to the All-Star break, Will Sammon of The Athletic reports.
The Mets optioned Butto to Triple-A Syracuse on Wednesday.
Butto (1-3) took the loss Tuesday against the Phillies, allowing two runs on one hit and four walks over five innings. He struck out four.
Butto (1-2) got the win Tuesday over the Cardinals, allowing three runs on five hits and three walks while striking out three over five innings.
Butto (0-1) took the loss Friday as the Mets fell 4-2 to the Cardinals, giving up four runs on four hits and three walks over 5.2 innings. He struck out four.
Butto was recalled from Triple-A Syracuse to start Sunday's game against the Royals.