Texas Gov. Rick Perry has asked the U.S. Department of Homeland Security for nearly $350 million to cover the costs he says Texas has incurred incarcerating illegal immigrants in state prisons and county jails.

In a letter to Homeland Security Secretary Janet Napolitano, Perry reiterated a claim he's often leveled against the federal government: that it's not doing enough to secure the border with Mexico and as a result, has allowed illegal immigrants to enter the U.S. and use taxpayer-funded resources, including the prison system.

The letter was dated Aug. 10, three days before the Republican governor formally announced he is running for president.

Reached after-hours Friday by phone, DHS spokesman Matthew Chandler said he wasn't in position to comment and said he could not confirm that the DHS had even received the letter.

Perry has been criticized by some fellow conservatives as being too lenient on illegal immigration issues. Unlike fellow GOP presidential hopeful Rep. Michele Bachmann, Perry does not think the U.S. should build a wall spanning the entire Mexican border. Perry also has supported discounted tuition rates for the children of illegal immigrants at Texas universities, and he has said Arizona's tough-on-immigration law wouldn't be right for Texas.

As governor, Perry was one of the first to talk about immigration by breaking out the issue of border security, a move that has won him support from conservative Hispanics. But he angered Hispanic leaders in June by endorsing legislation that would have prohibited cities from adopting "sanctuary" rules for handling suspected immigrants.

In his two-page letter to Napolitano, Perry described the formula used to come up with his $349.2 million bill, including $94.4 million to cover costs incurred by county jails.

"During tough economic times, when communities are making difficult decisions about their own budgets, Texas counties are being asked to cover more than $94.4 million in direct costs related to housing illegal immigrants while the state has been left to cover more than $254.8 million in such costs."

He included a memo from Comptroller Susan Combs in which she supports his calculations but warns that the estimates are conservative.

"The longstanding failure of the federal government to secure our border with Mexico continues to burden local communities and resources in Texas," Perry wrote. "Because there are not enough troops on the ground, illegal immigrants are able to penetrate the Texas border every day and use taxpayer-funded resources."

Perry is not the first governor to try to bill the federal government for the costs of incarcerating illegal immigrants. Arizona Gov. Jan Brewer, a Republican, sued the DHS in February seeking compensation for incarceration costs, among other things. And Napolitano herself, who preceded Brewer as Arizona governor, regularly sent the Justice Department invoices seeking such reimbursement before she became Homeland Security secretary.