TEL AVIV, Israel—Prime Minister Benjamin Netanyahu’s opponents pushed Thursday for a quick parliament vote to formally end his lengthy rule, hoping to head off any last-minute attempts to derail their newly announced coalition government. The latest political maneuvering began just hours after opposition leader Yair Lapid and his main coalition partner, Naftali Bennett, declared they had reached a deal to form a new government and muster a majority in the 120-member Knesset, or parliament. The coalition consists of eight parties from across the political spectrum with little in common except the shared goal of toppling Netanyahu after a record-setting 12 years in power. The alliance includes hardliners previously allied with Netanyahu, as well as center-left parties and even an Arab faction—a first in Israeli politics. Netanyahu lashed out at his foes on Thursday, signaling that he will continue to exert pressure on former allies who joined the coalition. “All members …