The announcement shocked Wall Street and adds to the merger mania already rampant in American retail banking, where size is seen as vital for survival.
Wells Fargo expects to make cost savings of $700m a year by closing down overlapping operations, echoing claims by Lloyds Bank in Britain that it would save pounds 350m a year from its own proposed merger with TSB. First Interstate has given the bid a cool response.
American banks are facing intense competition not only from banks at home and abroad but also from industrial giants such as General Motors and AT&T, which have huge credit card businesses, and from brokerage houses that offer services similar to those offered by banks.
First Interstate and Wells Fargo had been talking about a merger, but Wells' lucrative offer puts pressure on the Los Angeles-based First Interstate to succumb, in a move described by analysts as "a bear hug".
San Francisco-based Wells Fargo, the nation's 17th-largest bank, has proposed to exchange five-eighths of a share for each share of First Interstate, representing a price of $133.50 a share, 26 per cent higher than First Interstate's closing share price on Tuesday.
The combined bank would have $107bn in assets and nearly 2,000 offices, before branch closures.
News of the hostile bid sent US bank shares soaring. First Interstate's shares shot up 28.8 per cent to $136.50 yesterday afternoon on the New York Stock Exchange. Wells' shares jumped 5.7 per cent to $225.75.
"The economic benefit of the proposed merger is significant for shareholders of both companies," said Paul Hazen, chairman and chief executive of Wells.
William Siart, chairman of First Interstate, said: "I am deeply disappointed that Wells Fargo would take this uninvited action."