The Nasdaq Stock Market's 950-pence-a-share offer for the London Stock Exchange is an "attractive" one for shareholders, the US firm has said.
The LSE recently fought off a hostile bid from Macquarie
The comments came as the London Stock Exchange (LSE) rejected the £2.43bn ($4.2bn) takeover approach, saying it "substantially" undervalued the firm.
Nasdaq's surprise approach means the LSE has now been pursued by three of the world's biggest stock exchanges.
It recently fought off a 580p-a-share bid from Australia's Macquarie Bank.
Circle of suitors
German rival Deutsche Boerse made a £1.35bn takeover approach in 2004 before walking away after protests from shareholders, while Paris-based Euronext also expressed an interest.
The Nasdaq has more than 3,200 firms listed, including Google, which chose the exchange for its landmark market debut in 2004.
"The Board of London Stock Exchange firmly believes that the proposal, which represents only an 8% premium to the current market price, substantially undervalues the company," the LSE said in a statement.
The LSE also said it was still on track to return £510m to shareholders, a promise it made after fighting off Macquarie's bid.
"The board has rejected this unsolicited approach and intends to continue with its proposed 200p-per-share capital return."
But Nasdaq responded to the rejection by saying it had made an "attractive offer" with "unique benefits" not offered by other would-be buyers.
"Nasdaq and LSE are both pre-eminent equity markets in their respective countries," it said in a statement.
"Nasdaq believes that bringing together the two organisations would present listed companies, traders and investors with an equity market place, based on dynamic industry leadership to serve their needs, unmatched by any other market place in the world."
Shares in the LSE closed up 1.9% at 880p on Friday before the announcement was made, while Nasdaq shares jumped more than 10% to close at $43.56.
Analysts said that a tie-up between the two firms would lead to massive costs savings - as it could eventually lead to a single trading platform.
Experts also pointed out that a US bid would not face the same hurdles as Euronext and Deutsche Boerse.
Last year, UK regulators said they would back a takeover by either firm on condition that each company ensured the independence of the London exchange's clearing provider, Clearnet.