Valverde, with 288 career saves, last worked as a full-time closer with Detroit in 2012.
The right-hander earned two saves last year for the New York Mets but had a 5.66 ERA in 21 games. Washington signed him to a minor league deal last week, but the team did not announce the move.
Valverde went to spring training this year on a minor league contract with San Diego, but the Padres released him on April 2.
The Nationals are without veteran relievers Craig Stammen and Casey Janssen as both recover from injuries. Opponents are hitting .269 against Washington relievers, the majors' third-highest average allowed by a bullpen.
Washington recalled reliever Sammy Solis from Double-A Harrisburg and outfielder Michael Taylor from Triple-A Syracuse on Wednesday as the team placed outfielder Reed Johnson on the 15-day disabled list and optioned rookie starter A.J. Cole to Syracuse.
Johnson strained his left leg while running in a pinch-hitting appearance Tuesday. He left the game and was replaced on the bases by starting pitcher Doug Fister.
Cole made his first career start in the 13-12 win over Atlanta. Filling in for injured ace Max Scherzer, Cole received no decision after allowing nine hits and nine runs -- four earned -- in two innings.