By Lawrence Hurley and John Whitesides

WASHINGTON (Reuters) - Republican Donald Trump thrust the U.S. Supreme Court into the presidential campaign debate on Wednesday, rallying conservatives with a call for Justice Ruth Bader Ginsburg to resign after she lambasted him in a series of media interviews.

The presumptive Republican presidential nominee led a chorus of outrage over the comments by Ginsburg, who described Trump as a "faker" and speculated about the possibility of moving to New Zealand if he won the White House.

In a post-midnight counterattack on Twitter, Trump said the 83-year-old leader of the court's liberal wing had "embarrassed all by making very dumb political statements about me. Her mind is shot - resign!"

The furor gave Trump a cause to help galvanize conservatives divided over his unorthodox candidacy but concerned that the high court is too liberal, a mistrust fueled by recent rulings upholding racial preferences in university admissions and striking down tough abortion restrictions in Texas.

In three recent interviews, Ginsburg questioned how Trump had gotten away with not turning over his tax returns and said she could not bear to think about the wealthy real estate developer winning the White House.

In response, Trump said Ginsburg had politicized the Supreme Court with her comments and suggested she owed her fellow justices an apology.

"I'm questioning her mental capacity," he told Fox News Channel on Wednesday. "For her to have done that is an absolute disgrace to the Supreme Court."

Other Republicans jumped to join the attack, saying Ginsburg had proven she could not be an impartial voice on the country's highest court.

"For someone on the Supreme Court who is going to be calling balls and strikes in the future based upon whatever the next president or Congress does, that strikes me as inherently biased and out of the realm," Republican House of Representatives Speaker Paul Ryan said on CNN on Tuesday.

Senate Majority Leader Mitch McConnell called her comments "totally inappropriate," while Senator John Cornyn of Texas, the No. 2 Senate Republican, said Ginsburg's statements reflected poorly on her objectivity.

The New York Times and Washington Post joined in the rebukes, with the Times asking her to uphold the court's tradition of silence in political campaigns and drop the "punditry and name-calling."

Ginsburg's comments could push some on the right who have reservations about Trump into his camp, said Jonathan Adler, a conservative professor at Case Western Reserve University School of Law who is not a Trump supporter.

"There are some (not me) who learn to like Trump based on the enemies he makes," he said in an email.

The controversy erupted as Trump prepared for the opening of the July 18-21 Republican convention, which will formally make him the party's presidential nominee in the Nov. 8 election.

Ginsburg is the senior liberal on the court, which has been ideologically split between four liberals and four conservatives since conservative Justice Antonin Scalia died in February.

"This gives Trump the ability to attack not only Justice Ginsburg but ultimately the authority of the Supreme Court. That is a very bad situation," said Richard Painter, a law professor at the University of Minnesota Law School who served as a lawyer in the White House under Republican President George W. Bush.

JUDICIAL CODE

U.S. Supreme Court justices are not required to follow the code of judicial conduct that applies to judges on lower federal courts. The code, set by the U.S. Judicial Conference, says judges should not "make speeches for a political organization or candidate, or publicly endorse or oppose a candidate for public office."

Still, the justices typically try to stay out of the political fray.

The court has a sometimes pivotal role as a judicial counterweight to the executive and legislative branches of government, deciding some of the most divisive social issues in American life. In recent years, major rulings legalized gay marriage nationwide and upheld Democratic President Barack Obama's healthcare overhaul.

In public remarks earlier this year, Chief Justice John Roberts stressed it was important for the justices not to be seen as political players, saying criticisms of partisanship, which he described as inaccurate, were damaging to the court’s reputation.

"We don’t work as Democrats or Republicans," he said.

Ginsburg was not immediately available for comment on Trump's remarks and the other rebukes.

The high court, whose nine justices are nominated by the U.S. president to lifetime appointments, had already been caught up in political controversy as the Republican-controlled U.S. Senate refused to take up Obama’s nominee to replace Scalia, Merrick Garland.

Republicans have said the next president should be allowed to nominate a replacement for Scalia. Trump has emphasized the importance of naming conservative justices to the court.

The next president, potentially serving two four-year terms, could have the opportunity to appoint up to three new justices, not including Scalia's replacement. Ginsburg is the oldest of the justices. Justice Anthony Kennedy turns 80 on July 23, while Justice Stephen Breyer turns 78 in August.

Some Democrats defended Ginsburg, with U.S. Senator Jon Tester of Montana saying "she called him (Trump) for what she saw" and Senator Heidi Heitkamp of North Dakota saying, "I think she's the ultimate determiner of what's appropriate and what isn't."

But Democratic Senator Chris Murphy of Connecticut said, "I don't think we're well served by Supreme Court justices openly expressing their political opinions."

Asked about Ginsburg's remarks, White House spokesman Josh Earnest responded with a joke referencing a nickname used widely on social media by Ginsburg's admirers.

"She didn't earn the nickname 'the Notorious R.B.G.' for nothing," he said. The name was inspired by rapper Notorious B.I.G.

(Additional reporting by Emily Stephenson, Doina Chiacu and Caren Bohan; Editing by Frances Kerry and Jonathan Oatis)