WASHINGTON — A group of 20 apparel and footwear chief executives sent a letter to President Obama Friday, urging him to take immediate steps to restore full operation at the Ports of Los Angeles and Long Beach, where a strike has shut down most activity ahead of the crucial holiday season.

Calling the work stoppages at the nation’s busiest port complex “dire,” the executives — all members of the American Apparel & Footwear Association — expressed “grave concern” about the potential impact on their businesses and the broader economy, in their request for help from the federal government.

“As business leaders we must make decisions in a rapidly narrowing window of time whether to enact injurious contingency plans to accommodate our product shipments,” the industry executives said. “Recovering from Hurricane Sandy has put a toll on the U.S. economy and industry enough. To add to the burden with port shutdowns in major West Coast trade hubs is dangerous and irresponsible four our country’s health.”

Among the 20 executives who signed the letter were: Chip Bergh, president and chief executive office of Levi Strauss & Co.; Rick Darling, president of Li & Fung USA,; Rick Helfenbein, president Luen Thai USA; Ira M. Dansky, executive vice president and general counsel and secretary of The Jones Group, Inc.; Tom Glasser, vice president of VF Corp and president of its global supply chain; Kevin Burke, president and ceo of the AAFA; George Feldenkreis, chairman and ceo of Perry Ellis International and Michael Saunders, senior vice president and chief operating officer of Kellwood Company.

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The Los Angeles-Long Beach ports are the nation’s busiest and handle the largest volume of apparel, textiles and footwear — $40.3 billion in 2011, accounting for 31 percent of the sector’s imports, according to U.S. Customs & Border Protection.

The strike began on Tuesday (and continued through today without a resolution) after 67 workers from the International Longshore and Warehouse Union Local 63’s Office Clerical Unit walked out of negotiations and brought all activity to a standstill at the APM Terminal at the Port of Los Angeles. The rest of the 800-member clerical unit walked out on Wednesday and work stoppage spread to seven of the eight operating cargo terminals at Port of Los Angeles and three of the six cargo terminals at Port of Long Beach.

The ILWU’s 63-OCU division has been in negotiations with the Los Angeles/Long Beach Harbor Employers Association since June of 2010, when its last contract expired. The OCU claims shipping agencies and terminal operators, represented by the Harbor Employers Association, are trying to outsource their jobs to nonunion workers, a charge the Harbor Employers Association denies.