Payments firm Klarna launched its U.S business on Tuesday and said Overstock.com, one of the biggest U.S. online retailers, would be its first major retail partner.

The company, which has expanded in Europe and gained a 10 percent share of the Northern European e-commerce market, said it had partnered with around 10 U.S. merchants so far.

Sweden-based Klarna, founded in 2005 and backed by investors such as Sequoia Capital and Atomico, is now planning for rapid expansion in the United States, where it will take on rivals such as PayPal and Stripe.

"I would be disappointed if we didn't have hundreds of merchants on the platform doing millions of transactions as early as in 2016," Klarna North America CEO Brian Billingsley, told Reuters.

Klarna's services allow online consumers to buy goods by entering easy-to-remember details such as an e-mail address and zip code. It also lets consumers pay after delivery with Klarna assuming the risk in the interim and paying the retailer immediately.

Klarna, which had net sales of $319 million last year, said it was currently seeing "significant growth" in its core markets in the Nordics and Germany.

Asked how much the group could grow in 2016, Klarna CEO Sebastian Siemiatkowski said it was to early to tell as the U.S business was still in its infancy.

"There is definitely a potential to quickly reach half a billion dollars in revenue in a very short period of time," he said.

Klarna said the company would double in size if it was to capture half a percentage of the U.S market.

"And while of course our ambitions are much higher than half a percentage, it is definitely an interesting reflection of how extremely big the market is," Siemiatkowski said.

The company was valued at $2.25 billion in a recent transaction, according to Swedish tech news outlet Breakit. Its services are used by more than 50,000 retailers and transaction volumes processed by the company rose 150 percent last year.