By Mike Stone

(Reuters) - American International Group Inc <AIG.N> said on Monday it would sell its mortgage-guaranty unit to Arch Capital Group Ltd <ACGL.O> for about $3.4 billion.

AIG, the largest commercial insurer in the United States and Canada, said it would get $2.2 billion in cash, $250 million in Arch Capital's perpetual preferred stock and $975 million in non-voting common-equivalent preferred stock from the sale of United Guaranty Corp.

The Wall Street Journal first reported AIG's deal with Bermuda-based Arch Capital earlier on Monday, citing sources.

AIG said in January it would spin off the mortgage insurance unit, cut jobs and sell its broker-dealer network as part of a sweeping overhaul promised to shareholders to fend off activist investor Carl Icahn.

Later in March, United Guaranty filed for an initial public offering of up to $100 million with U.S. regulators.

Icahn, whose representative secured a board seat at AIG earlier this year, has been pushing the insurer to split itself into three smaller companies.

The billionaire saw it as a way for the company to shed its designation as a systemically important financial institution, which would free the company from having to comply with stricter capital requirements.

The insurer reported a bigger-than-expected quarterly operating profit earlier this month, driven by lower costs and strong underwriting.

Shares of Arch Capital and AIG were unchanged in after-market trading on Monday.

J.P. Morgan Securities LLC and Morgan Stanley & Co LLC advised AIG on the deal. Sullivan & Cromwell LLP was its legal adviser. Arch's financial adviser was Credit Suisse Group AG, with Cahill Gordon & Reindel LLP and Clyde & Co acting as legal counsel.

(Reporting by Sudarshan Varadhan in Bengaluru and Mike Stone in New York; Editing by Maju Samuel and Cynthia Osterman)