City officials have ordered the San Francisco Roman Catholic Archdiocese to pay nearly $3 million in health care costs for more than 1,000 employees after finding that it failed to make years of payments required by a pioneering local health care law.

San Francisco has also assessed the archdiocese $113,000 in penalties.

“It’s important for us to ensure that workers are made whole,” said Pat Mulligan, director of San Francisco’s Office of Labor Standards Enforcement.

The law, known as the Health Care Security Ordinance, requires businesses with more than 20 employees who work at least eight hours a week in San Francisco to make payments toward the workers’ health coverage, either by providing insurance or by paying into a health care savings plan. But a city audit of archdiocese records from October 2009 through June 2016 found that the religious organization had failed to make payments for a majority of its 1,722 employees covered by the law.

The archdiocese, which oversees Catholic institutions in San Francisco, Marin and San Mateo counties, disputes the city’s findings that it violated the law, spokesman Mike Brown said. Among other things, he said, the archdiocese contends at least some of the 1,086 employees did not work in San Francisco and therefore were not covered by the ordinance.

“While we don’t concede we are in violation, we also don’t believe that the numbers are correct, and we are working in good faith with the city to find the right figures,” Brown said.

Mulligan said the Office of Labor Standards Enforcement first notified the archdiocese of a “potential violation” of the law in 2012 and spent nearly four years making “continuous efforts to obtain complete, reliable data” from the religious organization.

After a series of incomplete responses, the archdiocese finally supplied new workforce data on Nov. 23, the labor office said. Based on those figures, the office told the archdiocese on Jan. 18 that it must pay $2.932 million to the 1,086 past and present employees by Feb. 21, and must pay the city an additional $113,000 in penalties for the violations.

The archdiocese could appeal the decision to the city controller’s office and, if unsuccessful, go to court.

The Health Care Security Ordinance, the first of its kind in the nation, has survived court challenges and could become a crucial source of insurance coverage in San Francisco if Congress and the Trump administration slash health funding to California and other states by repealing former President Barack Obama’s signature law.

Most of the archdiocese’s employees work at Catholic churches and schools. Out of 3,904 employees during the period covered by the audit, the city’s notice of violation said, 1,722 worked enough hours in San Francisco to be covered by the health care ordinance, and the archdiocese had made the legally required payments for only 636 of them.

The city also rejected the archdiocese’s assertion that 202 of its employees had waived health care coverage in 2012. The ordinance excuses an employer from providing coverage for employees who are already covered by their spouse, parents or another employer and voluntarily waive coverage. But the city said the archdiocese distributed a form telling employees they were exempt from the local ordinance if they were covered elsewhere, and failed to request a voluntary, signed waiver.

Policies of the archdiocese have been hotly debated since the 2012 papal appointment of Archbishop Salvatore Cordileone, an outspoken conservative, to lead the institution in one of the nation’s most liberal regions.

None of the previous disputes has involved the city. But City Attorney Dennis Herrera, speaking as a private citizen and church member, wrote an article in the National Catholic Reporter in 2015 denouncing Cordileone’s attempt to add a “morality clause” — forbidding homosexuality, fornication and other church-disapproved sexual conduct — to the rules governing Catholic high school teachers. Cordileone dropped the proposal before teachers approved their next labor contract.

Bob Egelko is a San Francisco Chronicle staff writer. Email: begelko@sfchronicle.com Twitter: @egelko