WASHINGTON — An epic Washington political battle took shape Sunday after the death of Justice Antonin Scalia as Senate Republicans dug in and refused to act on any Supreme Court nomination by President Obama. The White House vowed to submit a nominee within weeks.

Two senators seeking the Republican presidential nomination, Ted Cruz of Texas and Marco Rubio of Florida, both said unequivocally that the Republican-controlled Senate should ignore any nomination sent by Obama to Capitol Hill.

“The president can nominate whoever he wants, but the Senate is not going to act, and that’s pretty clear,’’ Rubio said on “Fox News Sunday.’’ “So, we can keep debating it but we’re not moving forward on it, period.’’

In an interview on ABC’s “This Week,’’ Cruz, a member of the Senate Judiciary Committee, said: “Let the election decide it. If the Democrats want to replace this nominee, they need to win the election.’’

In Saturday night’s Republican debate in South Carolina, Donald Trump called on the Senate to delay action on the nomination. Jeb Bush said it was Obama’s right to make a nomination but said he doubted the president would submit a consensus nominee.

The comments followed declarations by Senator Mitch McConnell, Republican of Kentucky and the majority leader, that Obama should not try to fill the vacancy left by Scalia, who died Saturday in Texas, given that less than a year remains in his second term.

That view is backed by Senator Charles E. Grassley, Republican of Iowa, chairman of the Judiciary Committee, which would consider any nominee. The stance puts Senate Republicans in the politically charged position of defying the president on a crucial court opening amid the heat of the presidential campaign — and while also trying to hold on to their majority in the Senate.

Democrats immediately sought to pressure Republicans, saying that a refusal to even consider a nominee would amount to an outrageous act of obstructionism.

Democrats predicted that a backlash from the public, particularly in the swing states where Republicans need to win to hold their control of the Senate, could eventually prompt reconsideration by McConnell.

“I think there is at least a 50-50 chance that pressure from the Republican Senate caucus will force McConnell to reverse himself and at least hold hearings and a vote,’’ said Senator Chuck Schumer of New York, a member of the Judiciary Committee.

Senator Elizabeth Warren, Democrat of Massachusetts, rejected McConnell’s call to allow the next president to appoint the new justice.

“Senator McConnell is right that the American people should have a voice in the selection of the next Supreme Court justice. In fact, they did — when President Obama won the 2012 election by 5 million votes,’’ Warren wrote on her Twitter page.

Scalia’s body was taken to a West Texas airport Sunday afternoon and was being flown to Virginia after it was determined he died of natural causes. Scalia’s family didn’t think a private autopsy was necessary and requested his remains be flown home as soon as possible, said Chris Lujan, a manager for Sunset Funeral Homes.

Scalia, 79, was found dead in his room at a West Texas resort ranch Saturday morning. Judge Cinderela Guevara of Presidio County, site of the ranch, told the Washington Post that he died of a heart attack.

In choosing a nominee, Obama could pick a liberal version of Scalia, which would fire up Democrats but would virtually assure that Republicans would block the nomination in the Senate.

Or he could choose a moderate — someone who came up as a prosecutor or a corporate litigator, with little record on culture-war issues — which could increase pressure on Republicans to allow a vote.

If Obama passes up the opportunity to put forward a progressive in favor of someone who represented corporations, it could provoke a backlash from the left and hurt Democrats in upcoming elections.

The two Democratic presidential candidates will have to take a stand on whomever the president nominates, and Senator Bernie Sanders of Vermont is challenging Hillary Clinton from the left and making the power of the corporate establishment an issue.

It was not clear which way the president was leaning. But some former White House officials said they would advocate a nominee with a proven record of support in Congress as a way of laying bare the purely political nature of the Republican opposition.

“There will be many opinions on this and a lot of good candidates,’’ said David Axelrod, a former senior adviser to Obama. “But I would favor sitting appellate judges like Srinivasan or Jane Kelly from the Eighth Circuit, who have cleared the Senate unanimously.’’

Sri Srinivasan, an Indian-American jurist whom Obama nominated to the US Court of Appeals, was confirmed by a vote of 97 to 0 by the Senate in May 2013. Kelly, a former federal public defender in Iowa who was in Obama’s class at Harvard Law School, was nominated to the Court of Appeals in 2013. Like Srinivasan, she was confirmed unanimously — in her case, 96 to 0.

Two other potential nominees are Patricia Ann Millet another judge on the US Court of Appeals for the District of Columbia, and Paul J. Watford, a judge on the US Court of Appeals for the Ninth Circuit.

The shock of Scalia’s death and the battle over whether to proceed with a confirmation threatened to upend McConnell’s careful plans to show that the Senate was working again after years of dysfunction. Republicans were eager for a relatively calm year leading into the election, but Scalia’s death ended those hopes.

Democrats said that if McConnell persisted in trying to block a nomination, he should anticipate little cooperation from them moving forward.

“If McConnell stonewalls, we will empty the arsenal,’’ said one top Democratic official, who requested anonymity to discuss party strategy. “We will make sure this is seen as the radical, unprecedented act of obstruction that it is.’’

Democrats said that they would welcome the opportunity to confirm a justice who would reshape the ideological makeup of the court with so many crucial decisions looming.

They said that if Republicans dismiss a nominee without a hearing or a vote, it would play to their political advantage and would motivate voters both in the presidential contest and the crucial Senate races in states such as Illinois, Wisconsin, Pennsylvania, Ohio, New Hampshire, and elsewhere.

Republicans said the fight would energize their voters as well and they would face a conservative revolt if they did proceed with a nominee, allowing Obama a late-term victory in potentially reshaping the court.