WASHINGTON — The Obama administration announced on Monday that it would postpone enforcement of a federal requirement for medium-size employers to provide health insurance to employees and allow larger employers more flexibility in how they provide coverage.

The delay is the latest in a series of policy changes, extensions and clarifications by the administration, and it drew a new round of criticism from congressional Republicans, whose scorching attacks on the law have become a central theme in many of this year’s midterm election campaigns.

The “employer mandate,” which was originally supposed to take effect last month, had already been delayed to Jan. 1, 2015, and now the administration says that employers with 50 to 99 employees will not have to comply until 2016 — allowing Democrats to placate business concerns and pushing the issue well beyond this year’s midterm elections.

In addition, the administration said the requirement would be put into effect gradually for employers with 100 or more employees. Employers in this category will need to offer coverage to 70 percent of full-time employees in 2015 and 95 percent in 2016 and later years, or they will be subject to tax penalties.