HARRISBURG — Gov. Tom Corbett received a one-month extension to tell the federal government whether Pennsylvania will be setting up a health insurance market under President Barack Obama’s health care law.

U.S. Health and Human Services Secretary Kathleen Sebelius told governors Thursday evening that the administration was delaying a Friday deadline to declare their intentions until Dec. 14. States can still opt to have theirs run by the federal government or join in a partnership with Washington.

Corbett administration officials have not said which direction they plan to take. But they say they have put off development of the online exchange because too many questions about its cost and other operational details remain unanswered.

“We are still looking at it and you’ve heard me say this before, I’m looking at the cost,” Corbett said. “I’m looking at the cost to Pennsylvania taxpayers and whether we can afford it. I have some ideas of where we’re going, but I’m not ready to announce it right now.”

Some Democratic lawmakers, insurers and hospitals want Corbett to set up a state-run system. The Washington, D.C.-based group Americans for Prosperity, which was founded by billionaire energy executives Charles and David Koch and spent tens of millions of dollars trying to defeat Obama in the election, has urged Corbett and other governors to reject it.