Democrats have secured control of the US Senate and been declared winners of the House of Representatives following major victories in Tuesday's midterm elections, delivering a significant political setback to President Donald Trump and his Republican Party.

The Associated Press confirmed that Democrats had won the Senate, flipping six Republican-held seats in Texas, Kansas, South Carolina, North Carolina, Ohio and Iowa.

In Texas, Democrat James Talarico defeated Republican Attorney General Ken Paxton, while former Democratic Senator Sherrod Brown returned to the Senate after defeating Republican incumbent Jon Husted in Ohio.

In South Carolina, paediatrician Annie Andrews defeated Republican candidate Darline Graham, who was appointed to the Senate following the death of her brother, Senator Lindsey Graham, in July.

Former North Carolina Governor Roy Cooper also defeated Republican candidate Michael Whatley, flipping another Republican-held seat.

In Kansas, Democrat Adam Hamilton defeated Republican incumbent Roger Marshall, becoming the first Democrat elected to the state's Senate delegation since 1932.

Iowa also recorded a Democratic victory, with Josh Turek defeating Republican Ashley Hinson in the race for the seat vacated by retiring Senator Joni Ernst.

The victories gave Democrats the 51 seats needed to secure control of the Senate, ending the Republicans' majority in the chamber.

Democrats also retained key seats in Georgia, where Senator Jon Ossoff won re-election, and New Hampshire, where Democrat Chris Pappas defeated Republican John E. Sununu in the race to replace retiring Senator Jeanne Shaheen.

In the House of Representatives, Democrats made significant gains, flipping more than a dozen Republican-held seats, according to the Associated Press.

They recorded notable victories in Iowa, where they captured three of the state's four congressional districts, which had previously been held by Republicans.

Democrats also won three Florida districts that Republicans had redrawn in an effort to improve their party's electoral prospects.

ABC News subsequently declared that Democrats had won control of Congress, reporting that the party's lead in the outstanding House races had become clear enough to secure a majority, although vote counting was still ongoing. The Associated Press had yet to formally call control of the House in its latest update.

The election results reflected widespread dissatisfaction with the direction of the country. The Associated Press Voter Poll indicated that many Americans were concerned about rising living costs, the war with Iran and corruption in government, with voters also favouring stronger congressional checks on the president.

Trump had campaigned extensively for Republican candidates, including Paxton, Husted and Graham, as he sought to maintain his party's control of Congress.

As the losses mounted on Tuesday night, the president took to social media to argue that he was not on the ballot and would have won by a landslide if he had been.

He also posted an image of a red cap bearing the word "VETO", signalling his intention to block Democratic legislation.

However, speaking to The New York Times on Tuesday night, Trump said he was willing to accept the election results and work with Democrats.

"I am absolutely willing to accept those results," he said, adding that his administration would look forward to working with the opposition party.

Trump also defended his administration's decision to go to war with Iran, describing it as a "very wise decision", and said he had no regrets about the Republican candidates he endorsed.

The Democratic victories are expected to reshape the political balance in Washington, giving the opposition party greater oversight of the Trump administration and the ability to challenge its legislative agenda during the final two years of his presidency.