US workers in the fast-food industry staged a one-day strike in dozens of cities on Thursday, calling for better wages and the right to unionise.

The strike was the largest so far in a 10-month campaign that began with 200 workers striking in New York last November, and which spread to Detroit and Chicago in July.

Organisers said the strikes, scheduled a day after the 50th anniversary of the March on Washington and a few days before Labor Day, were being held in 60 cities and had spread to the south – including Tampa and Raleigh – and the west, with workers in Los Angeles and San Francisco taking part.

In New York, the Democratic mayoral hopeful Christine Quinn took part in a march with several hundred workers and protesters before entering a McDonald's near the Empire State Building on Thursday morning.

Local organisers in Detroit said at least three stores had been shut down because of the strikes. One was a Checkers restaurant; the other two were Church's chicken restaurants.

The striking workers are part of a coalition of unions, campaign groups, clergy and community members. Fast-food workers are expected to be joined in some places by retail employees at stores owned by Macy's, Sears and Dollar Tree.

They want to form unions in order to negotiate higher wages without fear of recrimination. They are demanding $15 an hour, up from $7.25, the current minimum wage. The strikes come as the White House, members of Congress and some economists have called for an increase to $9 an hour.

The US labour secretary, Thomas Perez, said the strikes showed the need to raise the minimum wage. Perez told the Associated Press that for too many people, "the rungs on the ladder of opportunity are feeling further and further apart."

A New York-based group called Fast Food Forward, wrote an open letter to McDonald's, Wendy's, Burger King, Taco Bell, KFC, Pizza Hut, Domino's and Papa John's, pointing out the disparity between the profits made by fast-food companies and the wages they pay. It read: "Last year, your combined profits were $7.35bn. Yet you still paid most of your workers less than $11,200 a year – a poverty wage. It's shameful and outrageous."

Terrance Wise, 34, a father of three who works two jobs at Burger King and Pizza Hut in Kansas City, told the Guardian that twice as many people took part in Thursday's action than a previous strike in the summer. Wise said he was striking in support of a $15-an-hour wage, but also for "respect."

"We don't have a voice," said Wise, who is paid $9.25 an hour at Burger King and $7.40 at Pizza Hut.

The median wage for front-line fast-food workers, who are typically non-unionised, is $8.94 per hour, according to the National Employment Law Project, an advocacy group for lower-wage workers.

Fast Food Forward said workers were still being targeted for organising, including having jobs terminated and hours reduced.

Mary Kay Henry, president of Service Employees International Union, said: "The fast-food workers are fighting for all of us. SEIU members, like all service-sector workers, are worse off when large fast-food and retail companies are able to hold down wages and push down benefit standards for working people."

The National Retail Federation (NRF) dismissed the strike as "theatre orchestrated by organised labor".

In a statement, Bill Thorne, the senior vice-president of the NRF, said: "Retail and restaurant jobs are good jobs, held by millions of working men and women, who are proud of what they do for their customers and the communities they serve across America. The planned walkout is the result of a multi-year effort by big labor to diminish and disparage these hard-working Americans by attacking the companies they work for. "

McDonald's and Burger King said they did not set wage rates at the franchises that operate most of their outlets in the US.

McDonald's said in a statement that in its wholly-owned restaurants, pay starts at minimum wage but the range goes higher, depending on the employee's position and experience level. It said that raising entry-level wages would mean higher overall costs, which could result in higher prices on menus.

"That would potentially have a negative impact on employment and business growth in our restaurants, as well as value for our customers," the company said.