He blasted Republicans who plan to certify President-elect Joe Biden win as 'weak'
Thousands of pro-Trump protesters converged on Washington ahead of the session at his urging. Some clashed with police overnight.
Crowds gathered at the "Save America March" wore Trump-approved red baseball caps and cheered as Trump repeated the groundless conspiracy theories that have consumed his final days in office.
"You don't concede when there's theft involved," Trump said. "Our country has had enough and we will not take it any more."
Biden won the election by a 306-232 count in the state-by-state Electoral College and by a margin of more than 7 million ballots in the national popular vote, but the Republican president continues to falsely claim there was widespread fraud and that he was the victor.
A final outcome is not expected until later on Wednesday.
State and federal reviews have debunked Trump's claims of massive election fraud even as increasingly desperate legal efforts by his campaign and allies on the right to overturn the election have failed in numerous courts all the way up to the U.S. Supreme Court.
Biden is due to take office on 20 January, 2021.
Despite pressure from Trump to help overturn his election loss, Vice President Mike Pence, set to preside over the proceedings, will stick to his ceremonial duties and not block the congressional certification of Biden's victory, advisers said. Pence, a loyal lieutenant during the four years of Trump's tumultuous presidency, has no plans to intervene and has told Trump he lacks the power to do so, they said.
Meanwhile, the Dow and the S&P 500 rose, with investors piling into economy-linked financial and industrial stocks on bets that a Democrat-controlled Senate would lead to more fiscal stimulus and infrastructure spending.
Financials hit a 1-year high, while materials, industrial and energy sectors climbed over 1%.
Banks shares jumped about 5%, tracking a sharp rise in the benchmark 10-year U.S. Treasury yield.
The tech-heavy Nasdaq slipped 0.7% as behemoths Apple Inc , Microsoft Corp, Amazon.com Inc, Google-parent Alphabet Inc and Facebook Inc dropped between 1.6% and 2%.
Tesla Inc was the only major technology stock trading higher.
At 10:06 a.m. ET, the Dow Jones Industrial Average rose 260.13 points, or 0.86%, to 30,651.73, the S&P 500 gained 9.67 points, or 0.26%, to 3,736.53 and the Nasdaq Composite lost 88.86 points, or 0.69%, to 12,730.10.
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