By Clare Foran, Kristin Wilson and Annie Grayer, CNN

(CNN/WJZ) — The House voted 396-27 on Tuesday to pass a bill extending security protections to Supreme Court justices’ immediate family members.

The bill — the Supreme Court Police Parity Act of 2022 — will now be sent to President Joe Biden to be signed into law. It was introduced by Republican Sen. John Cornyn of Texas and passed the Senate in May.

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The bill has been in the spotlight following the bombshell leak of a draft majority opinion that would strike down Roe v. Wade, the 1973 Supreme Court ruling that legalized abortion nationwide. The leak has sparked public outcry and led to an increase in protests over the potential for the landmark ruling to be overturned.

Supreme Court justices are currently covered by federal security protection under US Code. The bill would extend those protections to immediate family members of the justices as well if the Marshal of the Supreme Court “determines such protection is necessary,” according to the text of the legislation.

Security protections surrounding the high court received fresh attention after the Justice Department charged a man who was arrested near Justice Brett Kavanaugh’s house in Maryland in June with attempting or threatening to kidnap or murder a US judge.

The House did not move immediately to take up the Senate bill, however, because Democrats had sought to change the bill to also include security for the family members of Supreme Court clerks and staff if deemed necessary by the Marshal of the Supreme Court.

But as calls from Republicans grew to pass the Senate bill through the House, House Speaker Nancy Pelosi informed her leadership team that the House would pass the Senate bill, according to a person who heard her remarks, a move poised to end an increasingly acrimonious standoff with Republicans over the issue.

House Majority Leader Steny Hoyer said Pelosi “was listening to the group” at the leadership meeting “to see how members felt” about moving the Senate bill — and the House version.

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“As all of you know, I would have preferred to move a bill which was a little more comprehensive,” Hoyer said on Tuesday.

Maryland Gov. Larry Hogan and Virginia Gov. Glenn Youngkin have called for “sustained resources” to secure the homes of justices, where demonstrators have protested the leaked draft.

Dozens of people have gathered outside the homes of Kavanaugh and Chief Justice John Roberts in the Maryland suburbs of Washington.

Demonstrations have also occurred outside the homes of justices Samuel Alito, Amy Coney Barrett and Clarence Thomas in Fairfax County, Virginia.

In a May letter to United States Attorney General Merrick Garland, the governors referenced a federal law that they say “prohibits picketing the home of a judge with the same to influence the judge’s decision-making process.”

“It is in our hands to ensure that applicable federal law is enforced to preserve the integrity of our American judicial system and the safety of our citizens,” Hogan and Youngkin said.

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On May 18, Garland said the U.S. Marshals Service started providing “around-the-clock security” at all the homes of the justices after the Department of Justice met with officials from the court.