Carl Icahn has taken a stake in eBay Inc and is proposing a spin-off of the its fast-growing PayPal division, but the e-commerce giant rebuffed the overture, setting the stage for a potential battle with the activist investor.

EBay, which bought PayPal for $1.5 billion in 2002 and has considered hiving off the multibillion-dollar payments service, argued on Wednesday that the business would lose synergies with the overall e-commerce business as an independent unit.

"First, eBay accelerates PayPal's success. Second, eBay data makes PayPal smarter. And third, eBay funds PayPal's growth," Chief Executive John Donahoe told analysts on a post-results conference call.

Some analysts, however, said that operating as a separate entity would encourage other online retailers to adopt the service and help retain key executives, with a spinoff that could unlock the value of a service that grew 19 percent during the holiday quarter.

Shares of eBay, which also reported earnings per share a penny above Wall Street expectations, jumped as much as 12 percent. The stock was up 7 percent at $54.41 after hours.

Donahoe said he had heard Icahn out but rejected his proposal. He added that the company intended to step up investments to safeguard the market position of the thriving payments service, which may exert pressure on margins.

Donahoe told Reuters in an interview on Wednesday that his company started seeking advice from its financial adviser, Goldman Sachs, five days ago, following Icahn's letter to eBay.

Icahn's proposal comes as the billionaire investor is urging Apple Inc to share more of its $146 billion cash pile with shareholders. The activist is demanding Apple do an additional $50 billion in share buybacks, which the company is advising shareholders to reject.

Icahn did not respond to requests for comment.

"I expect it to be a battle," BGC Partners analyst Colin Gillis said, citing eBay's longstanding opposition to a PayPal spinoff. "One of the reasons for that is because for commerce and payments, you need to remove as much friction from those two systems as possible. If you separate it out, you put more friction between" them.

PayPal started life as an independent company, founded in the late 1990s by technology entrepreneurs including venture capital investor Peter Thiel.

ECOMMERCE SUPREMACY

PayPal battled with eBay for supremacy in the then-emerging online payments market. But soon after it went public in 2002, eBay acquired PayPal for $1.5 billion. Today, its growth outpaces the rest of the company and it accounts for a large chunk of eBay's overall stock market value.

The unit has been a key driver of eBay's share value, as the company struggles to compete with larger rival Amazon.com Inc.

Analysts have estimated that PayPal, which already yields 40 percent of the company's revenue, may account for as much as half of the corporation's market value, which now stands at about $70 billion.

Icahn is known for decades of strong-arm tactics including proxy fights against major corporations. This month, he bought shares and derivatives giving him a 0.8 percent economic interest in eBay, and also nominated two of his employees to the eBay board. Those employees were not identified.

"Our directors have deep experience in the technology and financial services sectors, and a track record of value creation. This is the standard by which all future candidates will be assessed," Donahoe said on the call.

The eBay board includes prominent Silicon Valley venture capitalist Marc Andreessen, Ford Motor Co Executive Chairman William Ford Jr., and eBay founder Pierre Omidyar.

Donahoe, who spoke briefly to Icahn last week, told Reuters that he did not know Icahn's nominees and that the activist investor had not put forth any other proposals.

Revenue at eBay's PayPal division rose 19 percent during the holiday quarter, fueled by the growing use of mobile phones to shop. PayPal's total payments volume, a gauge of how much it is used to complete a transaction, rose 25 percent to $180 billion worth of transactions.

Companywide, revenue rose 13.5 percent to $4.53 billion for the quarter ended December 31.

For 2014, eBay forecast revenue of between $18 billion and $18.5 billion, while analysts expected a forecast of $18.5 billion, according to Thomson Reuters I/B/E/S.

Net income for the fourth quarter was $850 million, or 65 cents a share, up from $751 million, or 57 cents a share, a year earlier. Excluding some items, eBay earned 81 cents per share, a penny better than expected.

On Wednesday, the company also said it had authorized an additional $5 billion in stock buybacks.