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From the start, it was one of the most audacious takeover attempts in recent memory. An upstart French telecommunications company was trying this year to buy control of T-Mobile US, the big American wireless provider, for $15 billion.

By making an offer worth nearly as much as its own market value, the French company, Iliad, appeared to be a minnow trying to swallow a whale.

As if that weren’t ambitious enough, Iliad was doing so while T-Mobile US was in talks about a merger with Sprint, hoping to create a true third rival to Verizon Wireless and AT&T, the two largest American cellphone carriers.

But on Monday, Iliad’s odyssey came to an end. In a statement, the French company said was ending its efforts to take over T-Mobile US, despite having increased the size of the stake it was willing to acquire and the price it was willing to pay.

T-Mobile and its largest shareholder, the German telecommunications group Deutsche Telekom, were uninterested in the first offer, or a sweetened bid that was recently presented. As a result, Iliad ended its efforts “following exchanges with Deutsche Telekom and selected board members of T-Mobile US who have refused to entertain its new offer.”

In July, Iliad offered $15 billion for 56.6 percent of T-Mobile US, a surprising move that announced the global ambitions of Iliad, which has disrupted the market for cellphone plans in France.

Founded by Xavier Niel, a billionaire entrepreneur who is also an owner of the newspaper Le Monde, Iliad has taken share from established players by offering cheap cellular phone plans. That is similar to the strategy followed by T-Mobile’s chief executive, John Legere, suggesting the two companies might be a good cultural fit.

Iliad claimed it could create $10 billion in cost savings, an enormous number under any circumstances, and one that left many analysts puzzled, considering that the French company had no presence in the United States market.

T-Mobile US rejected the bid from Iliad, dismissing the French company as lacking credibility. Financing such a deal would have been difficult, saddling Iliad with billions of dollars in debt. And since Iliad made its original offer for T-Mobile, its market value has fallen steeply, complicating any potential offer.

Meanwhile, T-Mobile’s prospects of being acquired by Sprint fell apart later in the summer, after Sprint and its parent company, SoftBank of Japan, decided a combination was unlikely to win approval from antitrust regulators.

That left T-Mobile US pursing a stand-alone strategy, competing with Sprint for the spot of a distant third player behind Verizon Wireless and AT&T. Yet the prospect of a credible bid from Iliad lingered, at least until Monday.

Shares of T-Mobile US fell 2.5 percent on Monday, and were down a further 2 percent in after-hours trading.

On Monday, Iliad said it had increased its offer and was willing to acquire 67 percent of T-Mobile US, up from the original 56.6 percent, and that it was prepared to pay $36 a share, up from its original offer of $33 a share. But it said T-Mobile and Deutsche Telekom were uninterested in these terms, too.

“Iliad had the ambition to accelerate T-Mobile US’ transformation, notably by saving more than $2 billion of cost annually,” Iliad said in a statement. “This transaction would have created significant value for both Iliad’s and T-Mobile US’ shareholders. The Iliad Group will continue its profitable growth policy as it has been conducted over the last 15 years in the interest of its subscribers, employees and shareholders.”

T-Mobile US declined to comment, and Mr. Legere, a prolific user of Twitter, did not mention Iliad’s withdrawal in any of his tweets on Monday.

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