Soriano recorded two groundouts and a strikeout in a hitless frame against Syracuse, the Nationals' top affiliate, throwing just 11 pitches (eight strikes).
Yankees manager Joe Girardi was pleased that Soriano has successfully pitched in back-to-back games, but said that Soriano wouldn't be available to them until Wednesday, at the earliest.
New York has an off-day on Thursday, so the Yankees could also decide to hold off on activating Soriano until Friday, when the team opens a four-game weekend series with the Orioles.
Last year's American League leader with 45 saves, Soriano has been shelved since mid-May with right elbow inflammation. He also made two rehab outings at Class A Tampa before joining Scranton/Wilkes-Barre.
In the first year of a three-year, $35 million deal, Soriano was 1-1 with 5.40 ERA in 16 appearances for the Yankees before going on the disabled list.