The Nasdaq composite lost 0.92 per cent to 2,192.09 and the Standard & Poor's 500 index lost 0.64 per cent to 1,279.85.
JPMorgan Chase, the third largest bank in the US, announced on Sunday its deal to buy Bear Stearns, the fifth largest bank on Wall Street, for $236m, after it lost half its market value in Friday trading.
The offer, which has been approved by the Federal Reserve, values Bear Stearns at a price equivalent to $2 per share – just months after the bank's shares topped $170 each.
The losses sustained by Bear Stearns highlighted the continued pressure on US banks amid the global credit crunch.
The crisis was prompted when banks specialising in sub prime mortgage lending to people with poor credit histories were unable to recoup their initial outlay to debtors.
Bush's statement on the market came as the US Federal Reserve prepared to cut interest rates on Tuesday in an attempt to channel money into the US financial system.
The US Federal Reserve announced on Sunday that it would lower its emergency lending rate by a quarter point, to 3.25 per cent, in an attempt to bolster markets.
The Reserve also became a lender of last resort for Wall Street investment houses to begin securing short-term emergency loans.
The Bear Stearns sale and the US Federal Reserve strategy have highlighted the depth to which US financial markets have been exposed.
Simon Maughan, analyst at MF Global in London, said: "If you get a crisis of confidence in the wholesale banking space and something the size of Bear Stearns could go under, then people start to panic. You get a real fear factor."
Other banks are also facing a nervous future, with investors leaving Lehman Bros for fear it would be next to face a liquidity crisis.
The company registered losses of about 42 per cent in trading on Monday.
John Terrett, Al Jazeera's correspondent in New York, reported: "Today, Lehman Brothers had to come out and say 'look, we have had a tough time like everybody else, but we're going to be ok'.
"The management had to stave off a real head of steam that they are going to be the next bank to fall.
"But the management of Bear Stearns said they were going to be OK two days before they ran out of cash."
European banks - including UBS in Switzerland, HBOS in Britain and SocGen in France – also suffered losses of more than 10 per cent as concern affected global markets.
Some of Japan's largest banks also lost value, with Mitsubishi UFJ Financial Group, Mizuho Financial Group and Sumitomo Mitsui Financial Group down three per cent or more.
The pressure on banks is set to continue and is expected to prompt many to seek cash injections from sovereign wealth funds – large cash reserves held by rich countries.