If enacted, Los Angeles would join Seattle and San Francisco as some of the largest cities in the nation with phased-in minimum wage laws that eventually require annual pay of about $31,200.
Last year, Chicago passed a phased-in minimum wage increase to $13 an hour.
The Los Angeles council voted 14-1 after residents made impassioned statements for and against the plan that would progressively bump up the wage from the current $9 an hour, also the minimum for California.
"Today, help is on the way for the 1 million Angelenos who live in poverty," Mayor Eric Garcetti said.
The vote sent the measure to the city attorney to prepare a wage ordinance that will go to a council committee and, assuming it passes, to the full council for a final vote and then to Garcetti.
The vote follows months of debate and study at a time when American workers have struggled with flat wages.
Average hourly wages in the nation rose just 3 cents in April to $24.87. Wages have risen only 2.2 per cent over the past 12 months, roughly the same sluggish pace of the past six years, according to Labor Department figures.
The 9 million jobs lost during the recession have played a role in keeping wages down around the nation and even the recovery has had limited impact.
Yet pressure to raise the minimum wage has been building around the country and in Los Angeles, which has some of the highest housing costs in the nation.
Councilman Paul Krekorian said his mother raised a family while waiting tables for minimum wage.
"It would be a whole lot harder to raise a family now doing what she did ... because minimum wage has not kept up with the cost of living, with the cost of housing, with the cost of transportation or any of the other costs that we all have to bear," Krekorian said.
Nationwide, labour unions have been active in calling for increases and in organizing low-paid workers such as hotel cleaners, fast-food clerks and chain-store employees.
An ordinance passed last fall in Los Angeles raised the minimum wage to $15.37 an hour for workers at some hotels starting in July.
Nationwide events last month called on McDonald's, Burger King, Wendy's and similar companies to pay workers at least $15 an hour. Many fast-food workers currently earn close to the federal minimum wage of $7.25 an hour — about $15,000 a year for full-time work.
The Los Angeles ordinance would raise the minimum wage from $9 to $10.50 in July 2016, followed by annual increases until 2020. Nonprofits and businesses with 25 or fewer employees would have an additional year to reach the $15 plateau.
In many states, the push to raise local minimum wages is opposed by state officials concerned that such measures could create a confusing patchwork of pay rates.
The lone dissenting vote in Los Angeles came from Councilman Mitchell Englander, who said he felt raising the minimum wage above that of other Southern California communities might lead businesses to cut working hours and jobs and make it impossible for entire industries to do business.
"The very last thing that we should be doing as a city is creating a competitive disadvantage for our businesses with those in neighbouring cities and sending the clear message that Los Angeles is closed for business," he said.
The impact on cities of increasing the minimum wage is debatable, said Chris Tilly, director of the UCLA Institute for Research on Labor and Employment, which was involved in one study used by Los Angeles when considering its increase.
He said there haven't been a lot big cities that raised the rate and "none of them are for a city this big, that's this low-wage, with a minimum wage increase this size."
"This is something of an experiment," he said.
His institute concluded that hiking pay could result in some businesses cutting jobs but that would be offset because workers with more cash will spend it, increasing business demand.
Minimum wages in San Francisco and Oakland recently jumped to $12.25 an hour. A voter-approved measure will raise the wage in San Francisco to $15 in 2018. In April, Seattle began phasing in its new $15 minimum wage law which will take final effect in 2017.
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