By David Shepardson

WASHINGTON (Reuters) - Boeing Co's <BA.N> new chief executive, David Calhoun, assumed the job on Monday as the U.S. planemaker battles to recover from two fatal crashes of 737 MAX planes that killed 346 people in five months and led to the model's worldwide grounding in March.

Calhoun, 62, a longtime Boeing director named chairman in October after the board stripped Dennis Muilenburg of the title, was named chief executive on Dec. 23 following the firing of Muilenburg amid growing concerns about the company's relationship with regulators and its handling of the MAX.

Boeing has estimated costs of the MAX grounding at more than $9 billion to date and is expected to disclose significant additional costs during its fourth-quarter earnings release on Jan. 29. Boeing faces rising costs from halting production of the MAX this month, compensating airlines for lost flights and assisting its supply chain.

The company, which is due to report fourth-quarter earnings on Jan. 29, is also considering raising more debt and could announce its plans as early as this month, a source told Reuters.

Moody's on Monday said it had placed Boeing's A3 senior unsecured credit rating under review for a possible downgrade.

Recent developments, including layoffs at key supplier Spirit AeroSystems Holdings Inc <SPR.N> and the release of damaging messages between Boeing employees suggested a more costly and protracted recovery for the manufacturer to restore market confidence, Moody's said.

Calhoun, a former executive at Blackstone <BX.N> private equity group and experienced corporate crisis manager, is already working to repair the company's relationships with regulators, airlines and lawmakers. He previously headed a General Electric Co <GE.N> division that included airplane engines.

Calhoun told employees in an email on Monday he sees "opportunities to be better. Much better. That includes engaging one another and our stakeholders with greater transparency, holding ourselves accountable to the highest standards of safety and quality, and incorporating outside-in perspective on what we do and how we do it."

Last week, the board and its interim CEO reversed course and recommended regulators require simulator training for pilots before they resume flying the MAX. Directors also authorized the release of more than 100 pages of damaging internal messages that disclosed company efforts to avoid costly simulator training for the MAX amid troubling questions about its culture.

In one email, an employee said the 737 MAX was "designed by clowns who in turn are supervised by monkeys."A source close to Calhoun said on Sunday it was important employees saw the emails, which Boeing last week described as "completely unacceptable."

Calhoun wants to "get rid of the culture of arrogance" at Boeing that led to the messages written by a small number of employees, the source said.

U.S. Representative Peter DeFazio, who chairs the House Transportation and Infrastructure Committee, told reporters on Friday he advised Calhoun in a conversation he needs "to do something to relieve the pressure from Wall Street on your organization, which ultimately drove all this."

Richard Aboulafia, vice president of analysis at the Teal Group, said in an essay for Leeham News that Calhoun must decide "either to be a fantastic nine-month CEO, or he will stay on, becoming a potentially disastrous multi-year CEO." He argues "Boeing needs a CEO with an understanding of aviation markets, program management, and most of all, engineering."

On Friday, the board approved a $1.4 million annual salary for Calhoun and long-term compensation of $26.5 million if he achieves several milestones, including the return to service of the 737 MAX.

Three Democratic U.S. senators led by Ed Markey on Monday urged Boeing's board to cancel the payment tied to the MAX, saying it "represents a clear financial incentive for Mr. Calhoun to pressure regulators into ungrounding the 737 MAX, as well as rush the investigations and reforms needed to guarantee public safety."

Boeing defended the plan, saying it is "based on the fact that the safe return to service of the MAX is our top priority" and emphasized regulators "will determine the timeline for certification and return to service."

Reuters has reported the Federal Aviation Administration (FAA) is not expected to approve the MAX's return to service until at least February and potentially March or later. U.S. airlines have canceled MAX flights into early April or June.

Boeing is still working to complete a number of key hurdles on the MAX's return, including completing a software documentation audit with regulators and addressing potential wiring issues.

(Reporting by David Shepardson in Washington; additional reporting by Jamie Freed in Sydney; editing by Stephen Coates and Matthew Lewis)