Two Donald Trump-backed Republicans won special congressional elections in Florida on Tuesday, shoring up their party’s slim majority in the House at a crucial moment for the President’s domestic agenda.

Jimmy Patronis, the state’s chief financial officer, won the race to replace Matt Gaetz in the First Congressional District, on the western end of the Panhandle. With most of the vote counted late on Tuesday, Patronis had won 57 per cent.

State Senator Randy Fine captured the Sixth District seat that had been held by Michael Waltz, now Trump’s national security adviser. Fine had 56.7 per cent of the vote as of 9pm.

Both seats had been expected to remain in Republican hands, though some private polls showed Fine facing a close contest against Josh Weil, his Democratic opponent. Weil and Gay Valimont, the Democrat who ran against Patronis, each raised millions of dollars for their campaigns despite the Democrats’ struggles in Florida.

Both Patronis and Fine cleared their respective primary fields easily after securing Trump’s endorsement.

Fine’s margin — about 14 points with nearly all of the votes counted as of 9pm — was less than half of Waltz’s in November. Weil, in a statement after the results, called it “an incredible gain” for Democrats and “a warning sign” to Trump and his allies that voters would not support cuts to health care programmes and Social Security, among others.