UPDATE 2-First American bids for rest of First Advantage

(Adds stock prices)

NEW YORK, June 29 (Reuters) - First American Corp (FAF.N), which operates one of the largest U.S. title insurers, offered on Monday to buy the 26 percent of First Advantage Corp (FADV.O) that it does not already own for roughly $218 million of stock.

The transaction calls for First Advantage shareholders receive 0.5375 of a First American share for each of their shares. That values First Advantage at $14.04, which is 10.2 percent above the company's Friday closing price of $12.75 on the Nasdaq.

In morning trading, First Advantage shares rose $1.89, or 14.8 percent, to $14.64. Shares of First American fell 82 cents, or 3.1 percent, to $25.31 on the New York Stock Exchange.

A call to First Advantage was not immediately returned.

First American Chief Executive Parker Kennedy said the purchase would boost efficiency and "reduce organizational complexity," ahead of the company's plan to spin off its information solutions and financial services businesses.

First Advantage provides screening services, such as consumer credit, motor vehicle and employment background checks. The company is based in Poway, California, while First American is based in Santa Ana, California.

First American said the acquisition would boost earnings in 2010 and be subject to conditions including negotiation of a definitive purchase agreement. (Reporting by Jonathan Stempel; Editing by Lisa Von Ahn and Derek Caney)