Georgi Licovski/European Pressphoto Agency

LONDON – The Dutch telecommunications company KPN rejected an official offer from América Móvil, the Mexican telephone operator owned by the billionaire Carlos Slim Helú, continuing to say the 2.6 billion euro ($3.2 billion) bid was too low.

Now, KPN shareholders will have to decide.

On Tuesday, América Móvil, the owner of the Mexican wireless leader Telcel and the fixed-line carrier Telmex, launched a cash offer of 8 euros a share to increase its stake in KPN to 28 percent. The Mexican company currently owns a 4.8 percent stake.

The multibillion dollar offer, a roughly 25 premium to where the stock was trading before the proposal was announced in early May, would represent América Móvil’s largest expansion into Europe. It could also shake up the Continent’s competitive landscape, as most developed countries have three or four operators fighting it out in stagnant or slow-growing national markets.

In a statement, KPN took note of the start of América Móvil’s cash offer, but said the deal undervalued the company. KPN shareholders have until June 27 to accept América Móvil’s offer.

KPN has been fighting declining profit and revenue amid a domestic slowdown and the European economic crisis. The company’s share price has fallen 24 percent in the last 12 months. Shares rose 1.5 percent, to 7.7 euros, in Wednesday trading, still below the offer price.

“KPN will continue to explore all strategic options,” the company said in its statement. It has hired Goldman Sachs and JPMorgan Chase to act as financial advisers.

A spokesman for the Dutch company declined to provide more detail on its strategic options.

América Móvil has been considering a move for some time to provide geographic balance for its Latin American operations. In a previous statement to the United States Securities and Exchange Commission, the company said it aimed “to acquire an important minority stake in KPN, which has an attractive position in important European markets.”

Mr. Slim, the majority owner of América Móvil, also owns a stake of about 8 percent in The New York Times Company.