The body of late U.S. Supreme Court Justice Antonin Scalia was flown to northern Virginia from Texas late Sunday after investigators determined there was no foul play in the 79-year-old's death.

Jose Amezcua, a manager at Sunset Funeral Homes, told Fox News that he personally loaded Scalia's casket onto a private plane bound for Fairfax, Va. at El Paso International Airport. Terry Sharpe, assistant director for operations at the airport, told the Associated Press a private plane carrying Scalia's body departed around 8 p.m. EST. Scalia's body was accompanied to the airport by U.S. marshals.

Presidio County Judge Cinderela Guevara told Fox News that she determined Scalia had died of natural causes. Guevara also said that she had spoken to local investigators and U.S. marshals, as well as Scalia's family and personal physician, before determining that an autopsy was not necessary. 

Guevara said Scalia's doctor told her that the justice was suffering from minor ailments, but did not elaborate further. 

The owner of the Cibolo Creek Ranch, the West Texas resort where Scalia spent his final hours, told reporters Sunday that Scalia was part of a group of about 35 weekend guests and had arrived at the ranch at around noon Friday.

John Poindexter said Scalia ate dinner with the group and was his "usual, personable self". According to Poindexter, Scalia retired to his room at around 9 p.m., saying he wanted a long night's sleep.

Scalia was found dead in his room Saturday morning. Poindexter said he was found "in complete repose" and added it was obvious that he had "passed away without any difficulty" in the night.

Guevara says the formal declaration of death was made at around 1:52 p.m. Saturday.

A procession that included about 20 law enforcement officers brought Scalia's body to the El Paso funeral home more than three hours from the ranch. Kristina Mills, a history teacher at nearby Chapin High School, came to the funeral home to pay her respects and brought flowers.

"Recognizing his contribution to serving our country just compelled me to come," she told the Associated Press. "I wanted to do yellow roses because for him dying in Texas. I didn't want his family to have bad memories of Texas."

In the nation's capital, President Barack Obama ordered flags to be flown at half-staff at the high court, where Scalia served for three decades, and other federal buildings throughout the nation and U.S. embassies and military installations throughout the world.

Even while the flags were being lowered, the campaign-year political heat began to rise over the vacancy on the nine-member court.

At issue is whether Obama, in his last year in office, should make a nomination and the Republican-led Senate should confirm that choice in an election year. Obama pledged Saturday that he would submit a nomination to replace Scalia on the court "in due time."

The Constitution gives the Senate "advice and consent" powers over a presidential nomination to the Supreme Court. Ted Cruz, one of the two GOP senators running for president, told NBC's "Meet the Press" that the GOP-controlled Senate would be doing its job by blocking a nomination by a president with less than a year left in office.

"We're advising that a lame-duck president in an election year is not going to be able to tip the balance of the Supreme Court," Cruz said.

But the top Democrat on the Senate Judiciary Committee, which would hold hearings on a nominee, said it would be "sheer dereliction of duty for the Senate not to have a hearing, not to have a vote."

Vermont Sen. Patrick Leahy told CNN's "State of the Union" that he believes McConnell is "making a terrible mistake. And he's certainly ignoring the Constitution."

Fox News Channel's Casey Stegall and the Associated Press contributed to this report.