President Joe Biden's Democrats retained control of the US Senate on Saturday, a remarkable midterms election result that defied predictions of a Republican win over both houses of Congress.

Midterms traditionally deliver a rejection of the party in power, and with inflation surging and Biden's popularity in the doldrums, Republicans had been expecting to ride a mighty "red wave" and capture the Senate and the House of Representatives.

But the wave never got much beyond a ripple and on Saturday US networks called the key Senate race in Nevada for Democrat incumbent Catherine Cortez Masto, giving the party the 50 seats it needs for an effective majority.

The win clinches Democratic control in the Senate as Vice President Kamala Harris can cast the tie-breaking vote if the upper chamber is evenly split 50-50.

One Senate race remains up in the air -- a runoff in Georgia set for December.

The two parties had been neck-and-neck at 49 seats each after Democrat Mark Kelly was projected to win a tight Senate race in Arizona on Friday evening.

The result in the House of Representatives is also hanging in the balance, and while Republicans are slightly favored to take control, it would be with a far smaller majority than they had envisaged going into Tuesday's election.

- Call for unity -

In Arizona, Kelly called for unity in a victory speech on Saturday.

"After a long election, it can be tempting to remain focused on the things that divide us," he said.

"But we've seen the consequences that come when leaders refuse to accept the truth and focus more on conspiracies of the past than solving the challenges that we face today."

The former astronaut beat out challenger Blake Masters, who has not yet conceded defeat and was backed by Donald Trump.

The former president was omnipresent on the campaign trail and the Republicans' poor national performance was a damaging political blow.

Trump's response to the Arizona result was to double down on unfounded claims of ballot rigging, posting on his Truth Social platform that the Democrat's victory was a "scam" and the result of "voter fraud."

Trump is set to declare his 2024 White House bid on Tuesday -- an announcement he had planned as a triumphant follow-on to an expected crushing election victory by the party he still dominates.

The underwhelming outcome has prompted a bout of internal finger-pointing, with targets including Trump, the party leaders, and the campaign messaging.

US media on Saturday cited a letter circulated by three Republican senators calling for the postponement of party leadership elections currently scheduled for the middle of next week.

"We are all disappointed that a Red Wave failed to materialize, and there are multiple reasons it did not," the letter said.

"We need to have serious discussions within our conference as to why and what we can do to improve our chances in 2024," it added.

Some suggest Trump's early entry into the presidential race is designed to fend off possible criminal charges arising from multiple investigations into the final weeks of his presidency as well as his business affairs.

On Friday, Trump's lawyers challenged a subpoena from the Congressional committee investigating the January 6 attack on the US Capitol by his supporters.

The subpoena sought to have Trump questioned under oath next week but the lawyers filed a lawsuit arguing he enjoyed "absolute immunity" as a former president from being compelled to testify before Congress.

The subpoena is "invalid, unlawful, and unenforceable," the lawsuit said.