"Listen, Donald has been litigious for many, many years. He uses lawsuits to try to intimidate people and attack people," Cruz said Tuesday on conservative radio host Hugh Hewitt's show.
"If he wants to file a frivolous lawsuit, he can file a frivolous lawsuit," Cruz added. 
Cruz declined to say whether he thought Trump had standing to bring the lawsuit, which the outspoken billionaire businessman and political rival maintains he has. 
Trump has repeatedly threatened litigation over Cruz's eligibility, arguing he is not a natural born citizen because he was born in Canada to an American mother.
Supporters of Trump have filed a lawsuit challenging Cruz's eligibility to run for president, while another lawsuit has been filed to determine if Cruz is a natural born citizen.
"I think the lawsuit would be frivolous, and he’s not going to prevail. But sadly, whether a lawsuit is frivolous or not has not historically dissuaded Donald Trump from hiring plaintiff lawyers to go to court," Cruz said.