Square Inc., the mobile-payments startup founded by Jack Dorsey, is giving small merchants the ability to sell gift cards to shoppers on the go, stepping up competition with EBay Inc.’s PayPal business.

A new version of the Square Wallet app, which works with Apple Inc.’s iPhone and iPad as well as devices running Google Inc.’s software, lets users buy and redeem gift certificates in amounts from $10 to $1,000. Square enables retailers to accept payments with a device that plugs into a smartphone or tablet.

Gift cards are Square’s latest effort to convince customers to choose its fledgling service over PayPal Here, a mobile card reader that also works with smartphones and tablets. Square’s gift certificates may help the company gain share in the market for mobile payments, which Juniper Research estimates may top $170 billion in transactions by 2015, up from about $60 billion last year.

“These are mostly empowering merchants that haven’t had gift card programs,” Keith Rabois, Square’s chief operating officer, said in an interview yesterday. Any retailer that uses Square can offer gift cards through the application, with no additional setup required, he said.

Recipients of Square’s cards can integrate them into Apple’s Passbook app, which stores loyalty gift cards, digital tickets to movies, concerts and sporting events in one place. That makes it more likely that owners of Apple’s iPhone and iPad will try Square’s service.

“It’s clear that in 2012, the idea of a piece of plastic to redeem digital money is outdated,” Anuj Nayar, a spokesman for PayPal, said in an e-mailed statement yesterday. “Gift certificates live in PayPal’s digital wallet and can be spent wherever you can use PayPal, not just from a mobile device.”

Square, based in San Francisco, is processing about $10 billion in transactions on an annualized basis, about the same volume PayPal said in July that it anticipated for this year.

Both the Square and PayPal gadgets work with credit cards from Visa Inc., MasterCard Inc., Discover Financial Services and American Express Co.

Square’s push into gift cards follows other efforts this year to make its service more appealing to retailers.

The company in August revamped its transaction fees to offer merchants more flexibility, including an option for some businesses to forgo standard rates of 2.75 percent per credit- card swipe by instead paying $275 a month. PayPal’s fee is 2.7 percent.

Square also announced plans to process transactions in Starbucks Corp. stores, an agreement that included a $25 million investment from the retailer and added the coffee chain’s chief executive officer, Howard Schultz, to the startup’s board.

With increasing sales and customers, Square plans to move into bigger offices next year as the company expands its workforce to 1,000, more than double the current size. Square’s reader is used by about 2 million merchants and is available at Wal-Mart Stores Inc., Target Corp. and Apple outlets.

Dorsey, a co-founder of Twitter Inc., started Square in 2009.

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