The Virginia House of Delegates passed Tuesday a bill to award its electoral votes to the winner of the national popular vote as the newly elected Democratic majority sought to join the pact to leapfrog the Electoral College.

The state House voted 51-46 to enter into the National Popular Vote Interstate Compact, sending H.B. 177 to the state Senate despite opposition from Republicans who argued that the measure would upend the intent of the Framers.

The Electoral College is “part of a quaint thing that we used to call in civics class checks and balances,” said Del. R. Lee Ware, a Republican, on the House floor. “I hope you’ll stick with the checks and balances and not go along with H.B. 177.”

Democratic Del. Mark Levine, one of the bill’s two sponsors along with Del. Marcia “Cia” Price, argued that the Electoral College was a throwback that “began at a time when the founders actually didn’t think that there would be political parties.”

“They thought that a bunch of white men with property would get in a room in the back and they would decide who the president was,” Mr. Levine said during Monday’s floor debate. “It even had the infamous 3/5 clause, which meant that the more people were enslaved, the more slave owners had representation.”

If the bill is signed into law by Democratic Gov. Ralph Northam, Virginia would join 15 states and the District of Columbia in the agreement to have their electors cast their ballots for the presidential candidate who gains the most popular votes nationwide, instead of the statewide winner.

The compact would take effect after securing states with a combined 270 electoral votes, the number needed to elect the president. Virginia’s 13 electoral votes would bring the total to 209.

“We are determined to achieve 270 or more electoral votes,” said National Popular Vote chairman John Koza. “We will be dogged in our approach to attract Republicans, Democrats and independents who believe there is a better way to elect the President of the United States.”

The compact is billed as bipartisan, but support has come overwhelmingly from Democrats in blue states, spurred by the 2000 and 2016 presidential elections.

In those races, the Republican candidate captures the White House by taking the most electoral votes even though the Democrat won the popular vote. All but two states award all their electoral votes to the state winner, rather than divide them proportionately.

“Given the winner-take-all craziness of our Electoral College system, the Trump voters who chose Donald Trump in 2016 in the commonwealth of Virginia got zero votes toward the total,” Mr. Levine said. “I submit to you that that’s not fair.”

Republicans argued that compact, if enacted, would create chaos in the case of a very tight national race as well as shift the election focus to large urban areas like Los Angeles and New York City at the expense of low-population states and rural communities.

One Democrat joined Republicans in opposing the bill.

“Virginia currently assigns its electors to reflect the opinions of voters in the Commonwealth, and this bill might as well have an amendment stating that our electors will be chosen by the State of California,” said GOP Del. Israel O’Quinn in a statement. “Virginians should choose who gets Virginia’s 13 electoral votes — not a handful of large states.”

Nevada Gov. Steve Sisolak, a Democrat, made the same point last year when he vetoed a National Popular Vote bill, saying it would “diminish the role of smaller states like Nevada in national electoral contests and force Nevada’s electors to side with whoever wins the nationwide popular vote, rather than the candidate Nevadans choose.”

Four other Democratic-controlled states — Colorado, Delaware, New Mexico and Oregon — joined the compact during the 2019 legislative session.

“We are grateful to our sponsors in the Virginia General Assembly, and to citizens across the state who are making it clear that they prefer a national popular vote for president,” Mr. Koza said. “Regardless of party, the people of Virginia prefer a system where every voter, in every state, is politically relevant in every presidential election. National Popular Vote delivers on that promise.”