A statement from Culinary Union Local 226 said that more than 99 percent voted for the authorization.
The vote involved unionized workers at the downtown Binion's, El Cortez, Four Queens, Fremont, Golden Gate, Golden Nugget, Las Vegas Club, Las Vegas Plaza, Main Street Station and The D properties, the Margaritaville bar on the Strip, and linen service workers at Brady Laundries in North Las Vegas.
Khan said more than 5,000 members were eligible to vote. Balloting was held in two-hour shifts in the morning and evening at the East Las Vegas Community Center.
The Culinary is the largest union in Nevada, with some 55,000 workers including bartenders, food service workers, housekeepers, cooks, porters and others at casinos and properties downtown and on the Las Vegas Strip.
The union also represents some employees at McCarran International Airport and Valley Hospital Medical Center in Las Vegas.
Local 226 in Las Vegas is the largest local of the national UNITE HERE organization. Leaders have been negotiating with casino owners since contracts expired last summer.
Members last month voted to end a contract extension approved last June, clearing the way for strike and picket actions. Members previously approved a dues increase to cushion the financial blow of a walkout if one occurs.
Meanwhile, culinary and bartender unions reached agreement last week on a five-year contract with the LVH casino, formerly the Las Vegas Hilton.
MGM Resorts International and Caesars Entertainment Corp., which together control a majority of properties on the Strip, previously negotiated new five-year union pacts.
The independent Stratosphere, Riviera, Tropicana, and Treasure Island casinos have also settled.
The new contracts preserve health benefits and add measures to protect housekeepers from hazardous work conditions. The deals also aim to restore workers laid off when restaurants closed during the recession.
The last strike in Las Vegas ended in 1991, after workers picketed the Frontier casino for more than six years.