The Denver-based company, Dominion Voting Systems Inc, filed an earlier lawsuit against pro-Trump lawyer Sidney Powell, whom the company also accused of spreading false conspiracy theories about the election that Trump lost to Democrat Joe Biden.
A senior Dominion employee, Eric Coomer, also filed a defamation lawsuit against the Trump campaign, saying he had been driven into hiding because of death threats from Trump supporters.
Giuliani said in a statement that Dominion's lawsuit was intended to intimidate others from exercising their free speech rights.
"Dominion’s defamation lawsuit for $1.3B will allow me to investigate their history, finances, and practices fully and completely," Giuliani said, adding that he may file a countersuit against the company for violating his rights.
Trump and his allies spent two months denying his election defeat, and claiming without evidence that it was the result of widespread voter fraud, before his supporters stormed the Capitol on Jan. 6.
Dominion is seeking $1.3 billion in damages from the former New York City mayor, alleging in the lawsuit that "he and his allies manufactured and disseminated the 'Big Lie,' which foreseeably went viral and deceived millions of people into believing that Dominion had stolen their votes and fixed the election."
Dominion said it filed the lawsuit "to set the record straight" and to "stand up for itself, its employees, and the electoral process."
A group of prominent attorneys last week asked New York’s judiciary to suspend Giuliani's law license because he made false claims in post-election lawsuits and for urging Trump’s supporters to engage in “trial by combat” shortly before they stormed the U.S. Capitol on Jan. 6.
Dominion states in its lawsuit that it has spent $565,000 on private security to protect its employees, who are facing harassment and death threats.
“Giuliani’s statements,” the lawsuit stated, “were calculated to — and did in fact — provoke outrage and cause Dominion enormous harm.”
Founded in 2002, Dominion is a major U.S. manufacturer of voting machines, and various Dominion machines were used in more than two dozen states during the 2020 election.