EBay Inc. and activist investor Carl Icahn stepped up their attacks against one another in an escalating clash over the company’s board and its governance practices.

Icahn, who last month proposed that EBay spin off its PayPal electronic payments unit, published his third letter to shareholders in four days, in which he renewed his criticism of Chief Executive Officer John Donahoe and once again took aim at EBay directors Marc Andreessen and Scott Cook for what he called their “conflicts of interest.”

EBay’s founder and chairman, Pierre Omidyar, immediately fired back, calling Icahn’s claims “false and misleading.”

Icahn, 78, continued to press his allegations that Andreessen, a venture capitalist, unduly profited from EBay’s sale of videoconferencing-company Skype while he was on the board by participating in the acquisition of the unit and then selling it to Microsoft Corp. for a higher price.

Icahn also said having Cook, a director at Intuit Inc., on the board is tantamount “to having Pete Carroll, coach of the Seattle Seahawks, sitting in when the Denver Broncos were constructing their game plan for the Super Bowl.”

Icahn added that EBay hasn’t responded to his challenge to hold an open debate about the directors and questioned whether Donahoe is hiding “behind his legal army” in order to avoid addressing the issue.

In his response, Omidyar said Icahn is choosing to attack Andreessen, Cook and Donahoe “instead of having an honest discussion” about whether PayPal and EBay are better together.

“Scott and Marc are world-class directors with impeccable credentials. They have my full support,” Omidyar wrote. “John Donahoe has my full support, and the strong support of our board.”

EBay shares rose 1 percent to $57.93 as of 9:40 a.m. in New York.