Gov. Kemp led his former Democratic gubernatorial rival by 4 percentage points last week.
The Republican governor's position looks more precarious than before due to President Donald Trump's public criticism of his actions.
Several senior Republicans have dismissed Giuliani's unsubstantiated allegations of voter fraud in the 2020 election.
Kemp called the disputes over the results of the presidential election "a distraction" from Georgia's Senate runoffs next month.
Mike Lindell claimed that if Trump declares martial law in the seven states, his campaign allies could take control of the state's ballots and, apparently, overturn the results of the election in the president's favor.
The sitting president will host an event backing incumbent senatorial candidates David Perdue and Kelly Loeffler on January 4, the eve of Georgia's upcoming runoff elections.
The governor has come under fire following the election, with the state's result having gone in Joe Biden's favor.
The Trump campaign's legal efforts to challenge the results of the 2020 election have been unsuccessful.
"I feel we need to take steps to restore confidence in our elections," Georgia's secretary of state said.
"Never forget, vote them out of office!" the president tweeted Saturday morning, blasting a wide range of some of his closest political allies.
A spokesperson for Georgia's Republican attorney general said the Texas lawsuit is "constitutionally, legally and factually wrong."
The vast majority of states have certified the 2020 election results ahead of the non-binding deadline.
"There's a civil war brewing in Georgia for no good reason," Sen. Lindsey Graham said on Fox News' "Hannity" on Monday night.
"People are ANGRY!" President Donald Trump tweeted Monday about the results of the state's November elections.
The president has publicly argued with Governor Brian Kemp, a Republican, over Georgia's election results and subsequent ballot audits.
"Certifying the expressed will of the electorate is not irreparable harm, but rather inevitable and legally required within our constitutional framework," lawyers for Georgia wrote in a motion to dismiss Powell's lawsuit.
Trump criticized Kemp numerous times at the rally as he continued to pressure Georgia Republicans to support his efforts to flip the 2020 presidential election.
At a Georgia rally on Saturday, the president blamed Republican Georgia Governor Brian Kemp for allowing the "rigged" election.
Kemp's approval rating among Georgia Republicans since Election Day has fallen from 86 percent to 77 percent, according to a Morning Consult poll released Saturday.
In a tweet, the president called for Governor Brian Kemp and Secretary of State Brad Raffensperger to allow a signature verification.
The attorney L. Lin Wood also called on all rally goers to surround Brian Kemp's home and blare horns.
"We have an obligation to assure every Georgia citizen—regardless of ideology—that free and fair elections are what distinguish our Republic from all others," the former GOP officials wrote.
Trump criticized Governor Brian Kemp for allowing his state to be "scammed."
As the president continues to insist that Georgia's ballot recount must include repeated signature-matching procedures, he called for the governor's intervention on Monday.
The president suggested the Georgia Governor "overrule" the state's Secretary of State, as he continues to question election results amid a second recount.
"Man up, admit you got beat, and do what's right for our country," former Georgia Representative Allen Peake tweeted about the president's loss.
"Georgia's probably going to be the first state I'm gonna blow up," Powell said in an interview with Newsmax TV on Saturday night, referring to an upcoming lawsuit.
Videos show protesters upset about the election results, urging that Republican officials are not re-elected for "not explicitly helping Trump to 'stop the steal.'"
"At the end of the day, I've got to follow the laws of the constitution of this state and that's exactly what I'm doing," said Brian Kemp.