(Reuters) - J.C. Penney Co (>> J.C. Penney Company, Inc.) has started searching for a new chief executive to replace Myron Ullman, with top investor Bill Ackman pushing to have one named in 30 to 45 days, according to a letter the activist investor sent to the company's board.

Ackman, frustrated by the slow pace of the CEO search, also told fellow Penney board members that Allen Questrom, a former Penney CEO, would return as chairman if the department store operator chose a new CEO he liked.

"The CEO search process, which began in earnest three weeks ago, will be careful and deliberate to ensure we find the right long-term leader for J.C. Penney," Thomas Engibous, Penney's current chairman, said on Thursday evening.

Engibous also stressed that Ullman had the overwhelming support of the board and was "the right person to rebuild J.C. Penney by stabilizing its operations, restoring confidence among our vendors, and getting customers back in our stores."

The board "strongly disagrees" with Ackman and was "extremely disappointed" that his letter was made public, Engibous said. He also called Ackman's latest move "disruptive and counterproductive."

It is the second time since 2011 that Ackman has pushed for Ullman's departure.

Ullman, who was the CEO from 2004 to 2011, was brought back in April to stem a sales hemorrhage blamed on Ron Johnson, who was picked by Ackman in 2011 to remake the 111-year-old retailer as a trendier department store.

But on Johnson's watch, sales fell 25 percent last fiscal year as shoppers rejected his no-discounts pricing strategy and the company had to get $2.25 billion in financing to quiet concerns about its financial health.

Ullman's return was praised as a smart, but temporary, move in an emergency to repair relations with Penney's vendors and lift morale at the company.

He has largely brought back the deep discounting strategy Johnson jettisoned, but analysts this week downgraded Penney's stock on fears that the moves are not working fast enough.

IN PRAISE OF QUESTROM

The return of Questrom would be "the best thing to happen to J.C. Penney in a decade," said Sterne Agee analyst Chuck Grom, noting that the retailer had thrived during Questrom's tenure as CEO from 2000 to 2004.

J.C. Penney shares climbed 6.7 percent to close at $13.66 on the New York Stock Exchange.

"I am very concerned about the future of J.C. Penney," Ackman wrote.

Only recently has Penney selected a search firm, even though Ackman has been pushing since April for the search process to begin, his letter said.

Penney shares earlier this week hit their lowest levels since 2001. Analysts expect Penney to report that same-store sales fell 7 percent this quarter when it releases quarterly results on August 20.

In addition to the long struggle to win back shoppers alienated by Johnson's strategy, Ullman has had to contend with big holes in his management team. Only this week did Penney name a new marketing head after the role was vacant for 14 months. No one is heading its home goods section.

Questrom said on CNBC that a new CEO would need to have CEO experience, unlike Johnson, whose highest position before joining Penney was head of retail at Apple Inc.

Ackman said in his letter there are only likely "a handful" of executives who would fit the bill.

"We need a CEO with extensive, ideally department-store retail experience," Ackman said.

Saks Inc (>> Saks Inc) Chief Executive Steve Sadove, expected to step down once the luxury department store chain's acquisition by Hudson's Bay Co (>> Hudson's Bay Co) closes this year, declined to comment.

Brendan Hoffman, CEO of Bon Ton Stores Inc (>> The Bon-Ton Stores, Inc.), did not respond to a request for comment.

But some experts said another round of change at the top could hurt Penney at a time that it is preparing for the year-end holiday season, when many analysts expect it will finally begin to see sales recover.

"A new CEO would be disruptive because that would bring more change," said Walter Loeb, a veteran retail analyst, who said shoppers are beginning to come back to Penney.

Questrom told CNBC that Penney's board needs to act quickly and that he would only return as chairman if he was comfortable with the new CEO.

"They certainly don't have a sense of urgency, and if I had a company that was in this kind of trouble, I'd be much quicker to make a decision," he said.

Ackman's letter was first reported on by CNBC and later confirmed by a spokeswoman for Ackman's hedge fund, Pershing Square Capital Management.

(Reporting by Jessica Wohl in Chicago and Phil Wahba, Martinne Geller and Dhanya Skariachan in New York; Editing by Maureen Bavdek, David Brunnstrom and Jan Paschal)