LONDON, Dec. 12 — Nasdaq has started the takeover clock ticking for the London Stock Exchange today when it officially opened a $5.3 billion hostile offer.

Holders of shares in the exchange now have until Jan. 11 to tender their shares to Nasdaq, which is offering £12.43 ($24.44) apiece for them. Nasdaq, based in New York, already holds 28.75 percent of the London exchange, and needs to buy at least 22.25 percent more to get majority control. Nasdaq can extend the deadline once, to Feb. 10.

Robert Greifeld, chief executive of Nasdaq, said the offer represents “full and fair value” for the London exchange, balancing the current success of the business with new competitive threats. London now attracts more international listings than New York does, but it could lose some of that business to a pan-European electronic exchange that a group of giant investment banks are planning to set up.

Management at the London Stock Exchange quickly rejected the bid, as it did Nasdaq’s two previous overtures. “The board unanimously rejects Nasdaq’s offer, as it substantially undervalues the exchange and fails to reflect its unique strategic position and the powerful earnings and operational momentum of the business,” the London exchange said in a statement.