"On behalf of the court and retired justices, I am saddened to report that our colleague Justice Antonin Scalia has passed away," Chief Justice John Roberts said in a statement on Saturday, calling Scalia, 79, an "extraordinary individual and jurist."
Scalia's death was first reported by the San Antonio News-Express, who said he had apparently died of natural causes while visiting a luxury resort in West Texas.
Obama, who is traveling in California, extended his condolences, and the White House said he would have more to say about Scalia's death later on Saturday. The Supreme Court lowered its US flag in honor of the dead jurist.
CNN, citing sources, said Obama intended to nominate Scalia's successor, a move opposed by a number of leading Republicans, including Senate Majority Leader Mitch McConnell and Senate Judiciary Committee Chairman Chuck Grassley.
The looming political battle is almost certain to come up when six of the Republican presidential candidates participate in a televised debate Saturday evening in South Carolina, which holds its Republican nominating contest on Feb. 20.
"Justice Scalia was an American hero. We owe it to him, and the nation, for the Senate to ensure that the next president names his replacement," Senator Ted Cruz of Texas, a Republican White House hopeful, said on Twitter.
Signaling that Obama would face a stiff battle to win confirmation of a nominee before he leaves the White House next January, McConnell said in a statement that the vacancy on the high court "should not be filled until we have a new president."
Grassley, who heads the committee that will decide whether to send a nominee to the full Senate for a vote, said it was standard practice over the past 80 years to not confirm nominees during a presidential election year.
But Senate Minority Leader Harry Reid, a Democrat, said Obama should send the Senate a nominee "right away."
Obama could tilt the balance of the nation's highest court, which now consists of four conservatives and four liberals, if he tries to and is successful in pushing his nominee through the confirmation process.
"Unless he (Obama) can find a consensus choice, the next president will pick the replacement for Justice Scalia," said Senator Lindsey Graham, a Republican who also sits on the Senate Judiciary Committee.
POSSIBLE REPLACEMENTS
Appointed to the top US court in 1986 by President Ronald Reagan, Scalia was known for his strident conservative views and theatrical flair in the courtroom.
Scalia's replacement would be Obama's third appointment to the nine-justice court, which is set to decide its first major abortion case in nearly 10 years as well as key cases on voting rights, affirmative action and immigration.
Waiting for the next president to make a nomination would leave Scalia's seat empty for at least 11 months, an unprecedented gap in recent decades.
Obama's first two appointments to the court, liberals Sonia Sotomayor in 2009 and Elena Kagan in 2010, both experienced relatively smooth confirmation hearings in the Senate, which was then controlled by Democrats.
This nomination will be different, with Republicans now in charge of the Senate and keen to exert their influence over the process. Obama is likely to be forced into picking a moderate with little or no history of advocating for liberal causes.
Other factors the White House is likely to consider is whether to nominate a woman or a member of a minority group, or someone who fits into both categories.
Among those mentioned within legal circles as potential nominees are Sri Srinivasan, an Indian-American judge who has served on the US Court of Appeals for the District of Columbia Circuit since May 2013, and Jacqueline Nguyen, a Vietnamese-American who has been a judge on the San Francisco-based 9th US Circuit Court of Appeals since May 2012.
Paul Watford, a black judge on the 9th US Circuit Court of Appeals who was appointed in May 2012, and Jane Kelly, a white woman and former public defender who has served on the St. Louis, Missouri-based 8th US Circuit Court of Appeals since April 2013, also have been touted as possible nominees.
It has been nearly 50 years since political wrangling between a president and Senate pushed a Supreme Court nomination into the next administration.
In 1968, Chief Justice Earl Warren made clear his intention to resign and Democratic President Lyndon Johnson sought to elevate then-Associate Justice Abe Fortas, who had been a close confidant. Senate Republicans fought the nomination, claiming "cronyism," and Johnson withdrew it. The appointment fell to his successor, Republican Richard Nixon.