EBay Inc said it expects revenue at its PayPal unit to double by 2013 as it sought on Thursday to cast itself as a reinvented company and an innovator at the center of e-commerce.

Shares of eBay, which over the past two years has been seeking to shed an image of an Internet has-been, jumped nearly 8 percent following the PayPal comments during an investor meeting at its San Jose, California, headquarters.

The company expects PayPal's revenue to reach $6 billion to $7 billion by 2013, PayPal President Scott Thompson said. Revenue in the unit was $3.4 billion in 2010.

PayPal, which is used by 59 percent of the top 100 online merchants in the United States and 40 percent in Britain, is on track to gain market share of up to 24 percent by 2013, executives said.

Meanwhile, PayPal's merchant services business, which is geared to businesses, will be larger in 2013 than all of PayPal's business today, reflecting growth in that one channel, the company said.

No one has the breadth and depth of our capabilities, said Thompson.

EBay's two main businesses are its online marketplace, which remains in turnaround, and its fast-growing PayPal, an online payments company.

EBay investors are anxious to see stabilization and growth at the company's marketplaces site, which represents the bulk of revenue -- $5.7 billion in 2010.

Although eBay is making ongoing improvements, growth still lags that of overall e-commerce, which is dominated by main rival Amazon.com.

EBay was the pioneer of the Web auction during the dotcom boom, but the novelty of its marketplaces business eventually waned and shoppers complained that transactions were complicated and sometimes subject to fraud.

Since eBay last held an analyst day in March 2009, the company has worked to heighten trust and safety on its site while trying to update what many e-commerce experts have called the site's outdated search technology.

The majority of eBay's online buyers now make fixed-price purchases, which eBay says are more popular. The company has also been at the forefront of mobile applications, and consumers can use eBay's app and scan technology to compare prices on smartphones while shopping.

PayPal mobile transactions are estimated to double to $2 billion in total payment volume this year, executives said. The company has already announced that mobile on marketplaces will double to $4 billion in gross merchandise volume this year.

We are starting to play offense at this company, Chief Executive John Donahoe said.

EBay shares were up 7.5 percent at $34.33 in early afternoon.

(Reporting by Alexandria Sage; Editing by Tim Dobbyn and Matthew Lewis)