Justice Ruth Bader Ginsburg said Friday that she had had a recurrence of cancer but had been undergoing chemotherapy that had shown “positive results’’ and would remain on the court.

“I have often said I would remain a member of the court as long as I can do the job full steam,’’ she said in a statement issued by the Supreme Court. “I remain fully able to do that.’’

Ginsburg, who is 87, said she had begun a course of chemotherapy May 19, after “a periodic scan in February followed by a biopsy revealed lesions on my liver.’’

“Immunotherapy first essayed proved unsuccessful,’’ she said. “The chemotherapy course, however, is yielding positive results. Satisfied that my treatment course is now clear, I am providing this information.’’

She said a scan this month showed the liver lesions had been significantly reduced.

“I am tolerating chemotherapy well and am encouraged by the success of my current treatment,’’ she said.

Ginsburg is the senior member of the court’s four-member liberal wing. Were she to leave the court, President Trump would have the opportunity to nominate a third justice, joining Justices Neil Gorsuch and Brett Kavanaugh. A successful nomination would almost certainly move the court further to the right.

Ginsburg has had surgery for lung cancer and radiation treatment for pancreatic cancer in recent years. She also had surgery for early-stage pancreatic cancer in 2009 and treatment for colon cancer in 1999.

More recently, in May, Ginsburg underwent a gallbladder procedure, and she participated in oral arguments from her room at Johns Hopkins Hospital in Baltimore. On Tuesday, she was treated for a possible infection at the same hospital after experiencing chills and a fever, and she underwent an endoscopic procedure to clean out a bile duct stent was placed in August.

She left the hospital Wednesday and was “home and doing well,’’ a Supreme Court spokeswoman said.

“My recent hospitalizations to remove gall stones and treat an infection were unrelated’’ to the recurrence of cancer, Ginsburg said in her statement.

“I will continue biweekly chemotherapy to keep my cancer at bay, and am able to maintain an active daily routine,’’ she said.

If Ginsburg were to die or step down from the court there is little question Senate Republicans would try to confirm a Trump nominee even in the waning days of his first term.

“Oh, we’d fill it,’’ Senator Mitch McConnell of Kentucky, the majority leader, said last year.

Senate Republicans took a different approach after the death of Justice Antonin Scalia in 2016, refusing to consider the nomination of Judge Merrick Garland in the last year of Barack Obama’s second term.

McConnell and his allies say the two situations are different. When one party controls the Senate and the other the presidency, as in 2016, they say, vacancies should not be filled in a presidential election year. When the same party controls both the Senate and presidency, they argue, confirmations may proceed.

Democrats say this is hairsplitting hypocrisy that damages the legitimacy of the court. But their power to stop a third Trump appointment was diminished after changes in Senate rules on filibusters on nominations. All it takes now is a majority vote to confirm judicial nominees.

During the Obama administration, some liberals urged Ginsburg to step down so Obama could name her successor. She rejected the advice.

“I think it’s going to be another Democratic president,’’ Ginsburg told The Washington Post in 2013.

Trump, whose election proved her wrong, has been critical of Ginsburg, saying in 2016 that “her mind is shot’’ and suggesting that she resign. His sharp words came after Ginsburg criticized Trump in a series of interviews. She later said she had made a mistake in publicly commenting on a candidate and promised to be more “circumspect’’ in the future.

More recently, he urged Ginsburg and Sonia Sotomayor to recuse themselves in all cases involving him.