Fifteen states and the District of Columbia have established a health-insurance exchange, according to the nonpartisan Kaiser Family Foundation.

WASHINGTON — The Obama administration moved Friday to give states more time to submit plans for setting up insurance exchanges in 2013, a pillar of the health-care law.

These exchanges are designed to allow Americans who don’t get coverage through their job to buy insurance on Internet-based marketplaces, much as they shop for airlines tickets today. They were to be operated by states starting next fall so consumers could get insurance starting in 2014.

But just 15 states — including Washington — as well as the District of Columbia, have established an exchange, according to the nonpartisan Kaiser Family Foundation.

Several states, mostly led by Republican governors, have indicated they will not run an exchange.

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Ultimately, more than one-third of the states are expected to reject the option, forcing the federal government to step in and operate an exchange.

Governors were supposed to provide the Department of Health and Human Services a blueprint for setting up an exchange by Nov. 16. But with many states behind in planning, Secretary of Health and Human Services Kathleen Sebelius informed governors they could have until Dec. 14 to submit their blueprint.

States still must notify the federal government by Nov. 16 whether they intend to run and exchange or defer to the federal government.