UPDATE1- City National, Texas Capital offer stock to repay TARP

* Says offerings to repay TARP, bolster capital

* City National to offer 2.7 million shares

* Texas Capital to offer 3.5 million shares

May 4 (Reuters) - Regional banks City National Corp (CYN.N) and Texas Capital Bancshares Inc (TCBI.O) on Monday commenced public offerings to repay government aid received under the Troubled Asset Relief Program (TARP) and bolster capital levels.

Los Angeles-based City National, which has received $400 million as funds under the government's relief program, is offering about 2.7 million shares of its common stock, while Texas Capital will offer 3.5 million shares, the companies said in separate releases.

City National, the parent of City National Bank, said it intends to use proceeds toward the redemption of preferred stock and the repurchase of warrants sold to the Treasury Department as part of the capital purchase program.

Texas Capital, which had borrowed $75 million under the plan, said the offering will enhance its tangible common equity. It also plans to repurchase warrants issued under the government's program.

"With the consummation of this offering, we will be well positioned to continue to follow our quality growth strategy and to redeem the Capital Purchase Program funds when permitted by the regulators," Chief Executive George Jones of Texas Capital said in a statement.

Texas Capital and City National join a rising number of U.S. regional banks that are repaying funds received under government aid.