MONROE, La. (Reuters) - U.S. President Donald Trump struck a defiant note on Wednesday at a rally in Louisiana a day after Democrats clinched victories in a raft of local elections that cast a shadow over his 2020 re-election hopes.

Speaking at a packed arena in the city of Monroe, Trump doubled down on his assertion that a House-led impeachment inquiry into his presidency was a hoax and sought to buoy support for Republican businessman Eddie Rispone’s bid for the governorship.

“Eddie will defend your values from the all-out assault by the extreme left,” he said, describing incumbent Democratic Governor John Bel Edwards as “dangerously soft on crime.”

The remarks came after Democrats claimed an upset win on Tuesday in Kentucky over Republican Governor Matt Bevin after Trump campaigned for him, telling voters that pundits would say the president “suffered the greatest defeat in the history of the world” if he lost.

On Tuesday, Democrats also seized control of the state legislature in Virginia and gained ground in the key state of Pennsylvania, though Republicans held on to the governorship in Mississippi, where Trump also campaigned.

The loss in Kentucky may have raised questions about the success of Republican candidates who align themselves closely with the president. But Rispone, who also spoke at the rally, put himself squarely in the president’s camp.

“Louisiana is Trump country,” said Rispone, a little-known construction entrepreneur who will face off on Nov. 16 in a runoff election against Louisiana’s popular conservative Democratic governor, John Bel Edwards.

Slideshow ( 11 images )

Trump said he would return to the state next week for more campaigning.

Edwards, the only Democratic governor of a Deep South state, comfortably bested rival Rispone in a six-candidate primary last month, but he failed to secure the 50 percent needed to win a second term outright in Louisiana’s unusual primary system.

An observant Roman Catholic, Edwards opposes abortion, and this year signed a law banning the procedure after 15 weeks, which could have contributed to dimmed enthusiasm among Democrats.

“John Bel Edwards broke his solemn promise to the people of Louisiana when he rammed - that’s the only word I can say - rammed through the largest tax hike in Louisiana history,” Trump said on Wednesday. “How did you ever get a liberal Democrat to be your governor?” Trump asked thousands of fans waving Trump 2020 signs.

Edwards, for his part, has criticized what he called efforts to nationalize the state race but also promised to work closely with Trump, who carried the conservative-leaning state in 2016 by 20 percentage points, should the Republican win a second term.

Trump faces headwinds of his own, as Democrats in the House of Representative mount an impeachment inquiry into whether he abused his office by pressuring Ukrainian authorities to investigate political rival Joe Biden by withholding millions in aid.

Trump visited Louisiana last month ahead of the primary vote, later taking credit for forcing a run-off.

“The Governor of Louisiana, John Bel Edwards, has done a poor job. NOW HE IS IN A RUNOFF WITH A GREAT REPUBLICAN ... 66% DOWN TO 47% after I explained what a bad job the Governor was doing,” Trump wrote on Twitter.