WASHINGTON, May 21 (Reuters) - The White House believes the U.S. Federal Deposit Insurance Corp needs a "fresh start" with a new chair who is not part of the leadership that presided over its long-running cultural problems, a White House official told Reuters on Tuesday.

The administration is "very conscious" of the tight Senate calendar and wants to put a nominee in front of the Senate Banking Committee, which oversees the FDIC, as soon as possible, said the official who spoke on the condition of anonymity.

FDIC Chair Martin Gruenberg finally succumbed on Monday to a months-long scandal over sexual harassment and other misconduct at the agency, announcing that he would step down once the Senate has confirmed a successor. Gruenberg, a Democrat, had clung to his job since the scandal erupted in November, despite growing calls from Republicans and a handful of Democrats for his ouster.

A top U.S. bank regulator, the FDIC oversees lenders and insures Americans against the loss of their deposits. The agency faces a critical moment as regional banks remain under stress following last year's turmoil, and as it finalizes capital hikes and other major new rules for Wall Street banks just six months ahead of the U.S. presidential election.

Under the law, the only way for the Democratic administration to replace Gruenberg without losing control of the agency to Republicans is to confirm a new pick, putting the White House under unusual pressure.

Many Washington analysts believe Gruenberg may struggle to hold onto his job much longer, as Republicans continue to pile pressure on President Joe Biden to fire him.

An damning independent review this month found widespread misconduct at the FDIC went unaddressed for years, and cited instances in which Gruenberg - who has spent nearly two decades in leadership at the agency - lost his temper with subordinates.

"I don’t know who they’re going to find who can get the number of votes quickly and even if they find the perfect person, I wonder if that perfect person would be interested," said Isaac Boltansky, director of policy research for brokerage BTIG.

Gruenberg, 71, had been at the FDIC since 2005 and is the longest-serving FDIC board member in the agency's 89-year history. During that time he served as its chair twice - once under President Barack Obama and the second time under Biden.

While Gruenberg was not found to be directly responsible for the broad cultural issues at the agency, he apologized for misconduct that emerged under his leadership and for his own transgressions.

Should he leave the agency without a confirmed replacement, leadership of the FDIC would fall to Travis Hill, the agency's vice chair and a Republican who has voted against some of the proposed new rules. The agency would then be deadlocked 2-2.

Speaking to reporters earlier on Tuesday, White House press secretary Karine Jean-Pierre said "the president is taking this very seriously." (Reporting by Nandita Bose and Pete Schroeder in Washington; Additional reporting by Douglas Gillison in Washington Writing by Michelle Price Editing by Franklin Paul and Matthew Lewis)