* Judge sets hearing for 4 p.m. EST Tuesday
* Granting injunction against president would be "radical"
* Senator Warren says expects case will go to appeals court (Adds information on Mulvaney email, briefs filed by Warren and Republican states)
WASHINGTON, Nov 28 (Reuters) - The Trump administration warned that granting a temporary restraining order to prevent the president from naming an interim director of the U.S. consumer finance watchdog would be an extraordinary intrusion into the executive branch and harm the agency.
White House budget director Mick Mulvaney, appointed by Republican President Donald Trump to assume control of the Consumer Financial Protection Bureau (CFPB), was sued late on Sunday by an Obama-era appointee who argued that she is its rightful acting director.
In a filing in U.S. District Court in Washington just before midnight on Monday, the Trump administration responded to Leandra English's lawsuit seeking to block Mulvaney from becoming acting director of the agency, which he sought to abolish when he was a congressman.
The administration argued earlier on Monday that under the 1998 Federal Vacancies Act it has the right to appoint Mulvaney, adding it would be a "radical" step for a court to grant an injunction against a president and that doing so would harm him and the CFPB.
"A temporary restraining order would radically alter the status quo, disrupt the orderly operation of the agency, and throw into doubt whether the CFPB, under the leadership of an Acting Director, is accountable to the President, or to anyone," the filing said.
U.S. District Judge Timothy Kelly, a Trump appointee, set a hearing for 4 p.m. EST (2100 GMT) on Tuesday.
English was tapped on Friday by outgoing CFPB Director Richard Cordray, a Democrat appointed by the Obama administration, to lead the agency until a new director was confirmed by the U.S. Senate, a process that could take months.
Hours later, Trump said Mulvaney would lead the agency on an interim basis, sparking an unprecedented showdown.
The CFPB was created to crack down on predatory financial practices after the 2007-2009 financial crisis, but it is reviled by Republicans who say it is too powerful.
The president has a right to name a permanent director, officials agree, but there are competing legal claims over who should lead the agency in the meantime.
Both sides presented their arguments during an emergency hearing in U.S. District Court in Washington on Monday. Kelly said the issues raised were "extremely important and complicated."
Kelly and both sides said they hoped the case would be decided in the next few days.
In an interview with Reuters on Tuesday, Democratic U.S. Senator Elizabeth Warren, who conceived the CFPB, said she has "no doubt" the case will be appealed, regardless of which side prevails.
"It's too important to everyone to let it rest at the district court."
Warren - along with 24 other Congress members and former U.S. Representative Barney Frank, who co-authored the Dodd-Frank financial services overhaul law - filed a brief with the D.C. court in support of English on Monday. On Tuesday, West Virginia Attorney General Patrick Morrisey and Texas Attorney General Ken Paxton, along with six other Republican states, filed a brief in support of Trump.
Trump has long sought to weaken or abolish the 1,600-employee agency, saying too many regulations are suffocating lending.
Democrats say the agency needs to oversee consumer financial products such as mortgages and have power over large non-bank financial companies to protect borrowers.
On Tuesday, English was at work at CFPB headquarters "taking calls and meetings with external stakeholders and bureau staff."
Mulvaney again on Tuesday told CFPB staff to "disregard" instructions from English, who he said had sent at least one additional email on Tuesday "purporting to act as the Acting Director." (Reporting by Michelle Price, Pete Schroeder, Patrick Rucker and Makini Brice; Writing by Doina Chiacu and Michelle Price; Editing by Jeffrey Benkoe and Jonathan Oatis)