PHOENIX  Gov. Janet Napolitano is not counting on a new president to finally pay the bills she has been sending to Washington for years to cover Arizona’s cost of imprisoning illegal immigrants.

At least not immediately.

Napolitano said she’s going to continue to push for the federal government to pay money she believes Arizona is owed. But she said that has to take a back seat to the most pressing issue: the economy.

“I think we all have to agree that getting people back to work and getting this economy rolling again, getting construction projects moving, getting deals being done, getting jobs being created, that’s got to be his top priority,’’ she said. “And that’s important for Arizona, too.’’

But Napolitano said she eventually expects the new president  and the new Congress  to honor its commitments.

A federal law, the State Criminal Alien Assistance Program, requires the U.S. Department of Justice to reimburse states for the cost of incarcerating people in this country illegally who have been convicted of violating state laws. If there is no contract, the law says the U.S. government will “take the undocumented criminal aliens into custody.’’

Neither has happened. In the meantime, Napolitano has sent bills to the government.

That hasn’t deterred Napolitano from trying.

She continues to send bills on a regular basis. And the latest one to Attorney General Michael Mukasey is now approaching $501.3 million for costs Napolitano said goes back to 2003.

The bills are currently accumulating at the rate of about $10.2 million a month.

That is based on the state’s contention that the cost of the average inmate runs $58.21 a day. And there are more than 5,600 inmates who are here illegally — more than 14 percent of the approximately 39,000 people behind bars in state prisons.

Napolitano has said repeatedly that much of the state’s current $1.2 billion deficit could be solved if the government made good on its debt. And she said Friday that the failure of the feds to pay up is particularly unfair now, given Arizona’s budget crunch.

“We are subsidizing the federal government where immigration is concerned,’’ she said. “I’d like to see that stop.’’

And Napolitano said she intends to lobby the new administration to pay up.

“But I will tell you that, in the universe of issues, while that, I hope, will be a priority for the presidentelect ... I think we all have to agree that, for Arizonans and for the country, the economy has to be the top priority right now,’’ she said.