The council met Monday to hear from opponents and supporters and had been expected to clear the way for construction.
However, about one-third of the council's members were absent, so the vote was re-scheduled for next Monday in Upper Marlboro.
Supporters contend the casino near the nation's capital will be a big economic benefit to Maryland and the county. But opponents maintain it will create traffic problems and other headaches.
The county planning board approved the project on May 8, despite hearing complaints from residents and community leaders who objected to the building's lighting features and giant video screens.
Officials with MGM Resorts International say the video screens are an important part of the building's operation and design.
The company is planning a 300-room glass tower hotel and a complex with 3,600 slot machines, 140 gaming tables, a theater, several restaurants, a spa and high-end stores.
The MGM casino could open in July of 2016 if it receives the approval required from local officials to allow construction to begin within weeks. It would be Maryland's sixth casino.