WASHINGTON — Stymied by Republicans in Congress, President Obama has drafted an executive order to force any company that contracts with the federal government to issue paid leave to employees who are sick, are seeking medical attention or need to care for a sick relative.

The draft order, obtained by The New York Times on Wednesday, could affect hundreds of thousands of workers, because it would apply to federal contractors and their subcontractors. It would be the latest in a string of executive orders that seek to impose requirements on companies doing business with the government that the president and Democrats want applied nationally. The Labor Department was to approve the order and send it to the White House by Wednesday afternoon, according to internal communications viewed by The Times.

Mr. Obama has issued executive orders requiring federal contractors to recognize same-sex marriages, not discriminate against homosexual employees and pay required overtime. Last year, he raised the minimum wage for federal contract employees to $10.10 an hour.

Mr. Obama even considered — then dropped — a requirement that federal contractors disclose political contributions.