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Sprint and T-Mobile US have been slowly dancing toward a $32 billion merger of the third- and fourth-largest cellphone operators in the United States. Now a French upstart wants to break in on the cozy couple.

Iliad, France’s fourth-biggest mobile company, said on Thursday that it had made a $15 billion bid for a majority stake in T-Mobile US, a company that is roughly 60 percent bigger than it in market value.

“The U.S. mobile market is large and attractive,” said Iliad, which was founded by Xavier Niel, a billionaire French entrepreneur who is an owner of the newspaper Le Monde. “T-Mobile has successfully established a disruptive position, which in many respects, is similar to the one Iliad has built in France.”

Deutsche Telekom of Germany, the majority owner of T-Mobile US, which has long sought an exit from the United States, appeared cool to the idea of a new suitor. It has already turned down the bid, according to a person briefed on the matter.

Still, the approach could complicate the merger effort of T-Mobile US and Sprint as they seek to create a stronger No. 3 competitor to AT&T and Verizon.

Under the terms of the deal, Iliad said it would offer $15 billion for a 56.6 percent stake in T-Mobile US. The French company said it valued the remaining stake in T-Mobile US at $40.50 a share, based on unspecific cost savings totaling $10 billion to be created from the deal.

In total, Iliad said its offer valued shares of T-Mobile US at $36.20, a 17 percent premium on the carrier’s closing share price on Wednesday. Shares of T-Mobile US closed Thursday up 6.46 percent, to $32.94. The Wall Street Journal earlier reported the approach.

Iliad has gained market share in France by offering cheap deals and improved customer service compared with the country’s larger carriers, including the former state telecommunications monopoly Orange. Iliad ranks fourth in France, behind Orange, SFR and Bouygues.

In the first quarter of 2014, the latest figures available, Iliad had 14.3 million customers, including 8.6 million mobile subscribers and 5.7 million fixed-line users. By contrast, T-Mobile US has more than 50 million cellphone customers.

The French company, which has a market value of 11.9 billion euros ($15.9 billion), reported €1 billion in revenue during the first quarter of 2014.

Revenue at T-Mobile US, which has a market capitalization $25.3 billion, reached almost $7.2 billion during the second quarter of the year, the latest figures available.

Yet it is unclear how Iliad would achieve $10 billion in cost savings, since the French company has no presence in the United States. Analysts have reckoned that a merger of Sprint and T-Mobile US could produce cost savings in the tens of billions of dollars in large part from both companies cutting duplicate functions like marketing and back-office operations.

Buying a big stake in T-Mobile US could also test Iliad’s financial capabilities.

Iliad said that it would pay for the proposed deal through a combination of debt financing provided by a consortium of banks and an additional equity fund-raising worth about €2 billion.

Earlier on Thursday, the chief executive of T-Mobile US, John Legere, was asked in a conference call with analysts about the regulatory risk of a doing a deal. While saying that he would not comment on specific deals, Mr. Legere noted: “If you look at the long term of the wireless industry, it is a scale game.”

“We have been very successful, and we see a path forward to be highly successful as a stand-alone company, but we also know that we could significantly accelerate that growth, and create an even higher level of competition in the U.S. wireless industry, by various forms of accelerating this platform,” he said.