By Malathi Nayak

(Reuters) - T-Mobile US Inc <TMUS.O>, the No. 3 U.S. wireless provider, wants to turn its monthly subscribers into shareholders by offering them a share in the company's stock for free, it said on Monday.

Shares of T-Mobile closed 1.3 percent lower at $43.07.

T-Mobile, which calls itself the "Un-carrier," said in a statement it would offer a full share of T-Mobile US (TMUS) common stock to millions of existing and new postpaid service customers. The so-called Stock Up plan is not available to prepaid customers.

"This has never been done before," by a public company, Chief Executive John Legere said on a media call after the announcement.

Legere has led the rollout of a series of consumer-friendly offers in the past three years, such as the free video streaming option "Binge On" and data rollover plans, some of which have been copied by rivals. These have helped T-Mobile gain market share as it fights a price war in an oversaturated wireless market with Verizon Communications Inc <VZ.N> and AT&T Inc <T.N>, as well as smaller competitor Sprint Corp <S.N>.

T-Mobile said in a statement it had also launched a T-Mobile Tuesdays app to give its postpaid and prepaid customers weekly perks such as free food, movie tickets and ride shares through partnerships with firms such as Domino's Pizza Inc <DPZ.N> and Lyft. It will also offer an hour of free Wi-Fi to customers on domestic flights that have Gogo Wi-Fi connectivity.

Postpaid customers who recommend T-Mobile to friends can get another share for every new user who signs up and can get up to 100 shares a year, the company said.

The latest offers will ensure T-Mobile customers stay with the carrier and recommend it to friends, Chief Marketing Officer Andrew Sherrard said in an interview. "Some (free offers) will cost us some money but over time we think it will be a really good investment."

T-Mobile will not be issuing new shares for the "Stock Up" plan, executives said on the media call.

T-Mobile's brokerage partner LOYAL3 will buy the carrier's shares and offer them to customers, they added, noting that the company would cover all associated charges.Bellevue, Washington-based T-Mobile, controlled by Deutsche Telekom <DTEGn.DE>, said it added 2.2 million customers on a net basis in the first quarter ended March 31.

(Reporting by Malathi Nayak; Editing by Andrew Hay and Richard Chang)