"We condemn the violence in the strongest possible terms," US Vice President Mike Pence, who is presiding over a session in the Senate, said in his remarks.
Senate Majority Leader Mitch McConnell, a Republican, also lashed out at protesters who stormed the Capitol and halted the Electoral College vote counting, while stressing that Congress will finish the certification of the results.
Members of the House of Representatives have also resumed their session.
The chambers were separately debating an objection to the counting of Arizona's electoral votes before police placed a lockdown on the Capitol due to the breaches.
