President Donald Trump and Republicans in Arizona and nationally are stoking claims of deliberate election fraud in the state's U.S. Senate race as Martha McSally and Kyrsten Sinema await results of a vote that could swing in either's favor.

The tight race has left Republicans in jeopardy of losing a Senate seat in the state for the first time in 30 years.

Though McSally held a lead in early-vote totals, the tally flipped in Sinema's favor Thursday night. Updated results Friday evening kept Sinema with a 20,000-plus advantage, but an estimated 360,000 ballots remain to be counted.

No group has brought forward allegations of specific criminal activity, although one Republican lawsuit addressed an equity issue over how early-ballot signatures are verified.

"Just out — in Arizona, SIGNATURES DON'T MATCH," Trump posted on Twitter on Friday afternoon. "Electoral corruption — Call for a new Election? We must protect our Democracy!"

Earlier, Trump told reporters it was "interesting" that the extended vote-counting "always seems to go the way of the Democrats."

"Now, in Arizona, all of a sudden, out of the wilderness, they find a lot of votes," Trump said. "And she's — the other candidate — is just winning by a hair."

MORE: Sinema's lead over McSally widens in roller-coaster U.S. Senate race

Amy Chan, former state elections director under Republican Secretary of State Ken Bennett, tweeted, "Unfounded allegations of voter fraud are totally irresponsible and should rightly be condemned because they shake voter confidence & can affect future participation. Voter fraud in my experience is almost nonexistent."

McSally, Sinema and their allies poured tens of millions of dollars into advertising to help lock down the seat. Although Republicans maintained control of the Senate in this week's midterm elections, any seat picked up by a Democrat would eat into their narrow margin.

Challenging the signature process

Local Republicans brought a legal case against Maricopa County Recorder Adrian Fontes and other county recorders over the inconsistent way counties verify signatures on mail-in ballots that are dropped off at the polls on Election Day.

When counties receive mail-in ballots, election workers attempt to check signatures against voters' signatures on record. If workers cannot verify a signature, the county attempts to contact the voter to allow them to confirm their ballot.

All of Arizona's 15 counties take part in this process before Election Day, but only a handful, including Maricopa County, allow voters to continue "curing" their ballots after Election Day.

U.S. Sen. Jon Kyl, R-Ariz., a McSally supporter, issued a statement critical of the inconsistencies in how county recorders handle ballots.

"Every single lawful vote in Arizona should be counted," Kyl's statement said. "And voting laws in our state should be applied uniformly across the map. Unfortunately, the Democrats' legal strategy sounds an awful lot like an effort to disenfranchise voters from 11 counties from rural parts of our state and that's troubling."

However, the election process of many of the counties that weren't curing are overseen by Republican county recorders.

The parties agreed to a settlement in court Friday that requires all counties to continue checking signatures until 5 p.m. Nov. 14.

Emergency-voting center allegations

On Friday morning, the Arizona Republican Party accused Fontes of "premeditated destruction of evidence" after "voting irregularities" in the election.

State Republican Chairman Jonathan Lines raised the level of accusations, saying Fontes, a Democrat, "cannot be trusted to administer elections in Arizona."

That accusation stems from a letter the party sent Fontes asking the county to set aside about 3,000 ballots cast at emergency-voting centers on the Saturday and Monday before the election.

This is the first year Maricopa County has offered emergency voting, but other counties have offered the extra polling hours for years.

In its letter, the Arizona GOP argued that state law does not allow recorders to offer early voting after the Friday before Election Day except in specifically defined emergency situations.

It asked the counties to "identify and segregate all ballots" cast at emergency-vote centers, but so far has not filed a lawsuit.

Fontes said the county counted the ballots but saved the envelopes in case they were needed in a future lawsuit.

"Keeping the ballots separate and uncounted is illegal, and I refuse to disenfranchise voters," he said. "So if they want to sue me for something, I understand the Clerk's Office is open until 5 p.m."

Rhetoric heats up Friday morning

Rhetoric about possible election fraud in Arizona, along with similar claims in Florida, reached the national level Friday morning.

In a tweet, Trump's campaign manager, Brad Parscale wrote, "These democrat counties in Florida and Arizona are playing tricks because they just can’t accept the fact they lost. I will not be shocked if investigations lead to rampant fraud."

Although Fontes is a Democrat, the Maricopa County vote in 2016 favored Trump by about 3 percentage points. Statewide, Trump won by about 3.5 percentage points.

Why does the count take so long?

Although the drawn-out counting process has frustrated both parties, it's largely the same as vote counts in many major elections in recent years.

MORE:Here's how to check if your early ballot was counted in Maricopa County

A large number of Arizona voters cast early ballots. These must be signature-verified and opened by a bipartisan board of election workers. That means many ballots turned in at the last minute take days or weeks to count.