The chambers each voted on the plan following a charge by a group of rioters to the Capitol building while other demonstrators assembled outside. It is unclear who induced the breach of the building.
The Senate overwhelmingly voted 93-6 against opposing counting of a slate of 11 presidential electors from Arizona for Democratic presidential candidate Joe Biden.
All votes in support of the objection came from Republicans. They were Sens. Ted Cruz (R-Texas), Josh Hawley (R-Mo.), Cindy Hyde-Smith (R-Miss.), John Kennedy (R-La.), Roger Marshall (R-Kan.), and Sen. Tommy Tuberville (R-Ala.).
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In the House, 303-121 voted against the objection.
Both chambers were set to resume their joint session.
Earlier during the joint session of Congress, Rep. Paul Gosar (R-Ariz.) and Cruz objected to Arizona’s 11 electoral votes, triggering debates by each chamber and a vote.
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More than 60 Republican House representatives joined Gosar and Cruz to oppose the slate of votes for Biden, leading to a suspension in the joint session and separate, simultaneous debates in the two chambers.
The objection requires a majority vote from both chambers to pass.
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The count of Biden's 306 votes to President Donald Trump's 232 was finished in steps that lasted until 3:40 a.m. Vice President Mike Pence addressed the results to cap a gloomy end to an unforgettable day in Washington.
Several moments later, Trump acknowledged the results and said "there will be an orderly transition on January 20th."
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In a statement released by the White House, the president again made allegations about the results of the election but said that this month will bring to an end "the greatest first term in presidential history."
Twitter had suspended Trump's account for 12 hours after he proceeded to promote his allegations of election fraud following the chaos at the Capitol.
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A woman was shot inside the Capitol by a police officer and later succumbed to her wounds, the National Guard was activated and the mayor dictated a 12-hour curfew in the city that began at 6 p.m.
Three other adults died after what is believed to be some sort of medical emergencies around the Capitol grounds, the Washington, D.C., police chief said.
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The disorders had prevented debate in both chambers about a Republican objection to the Arizona results, which in the end was soundly defeated.
In reconvening the Senate after an order has been restored, Senate Majority Leader Mitch McConnell, R-Ky., said the nation's government had faced down greater threats than what he called an "unhinged crowd."
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"I want to say to the American people: The United States Senate will not be intimidated," McConnell said.
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