The insurer American International Group Inc., which is being pressured by the government to divest assets, announced Thursday that it has agreed to sell its personal auto insurance unit to a rival, Zurich Financial Services AG, for $1.9 billion.

It would be the largest sale of an AIG business since the government bailed out the New York company.

Zurich Financial said the acquisition would make its Farmers Group Inc. subsidiary the third-largest U.S. personal-lines insurer. Zurich Financial already has extensive operations in many western states. It ranked second among auto insurers in Arizona, California, New Mexico, Oregon and Washington, and third in Texas, in 2007, the most recent year for which regulators have state-by-state data.

Zurich Financial is to acquire the AIG unit, which uses the trade name 21st Century Insurance, in two steps. First it would pay $1.9 billion for the division, then it would sell 21st Century's regulated insurance businesses to Farmers for $1.4 billion.

To boost Farmers' capital, Zurich Financial is expected to raise $1.1 billion in a stock offering to institutional investors. Farmers has an extensive network of agents, but 21st Century focuses on selling direct to consumers by telephone and the Internet. The deal implies that 21st Century's value has not changed over the past two years. AIG had previously owned more than 60% of 21st Century, and bought the remaining 39% in 2007 in a deal that valued the entire company at $1.9 billion, according to Thomson Reuters.

James Schiro, Zurich Financial's chief executive, said it has been seeking to expand its U.S. auto insurance business because it is a stable one that can balance out other, more volatile lines of revenue.

AIG is trying to sell off other units, including International Lease Finance Corp., its aircraft leasing business, for which a second round of bids are due in late April, according to a person familiar with the matter. But asset sales have been hampered by the poor economy, narrowing the pool of potential buyers for some of AIG's most prized assets.

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