"John McCain kept reciting to me names of dictators during that speech," CNN quoted the Minnesota Senator as saying on Saturday at a campaign event in Iowa.
"Because he knew more than any of what we were facing as a nation, he understood it... He knew because he knew this man more than any of us did."
Trump and McCain, the 2008 Republican presidential nominee, were frequently at odds over the former's approach to campaigning and eventually, his performance as President.
In 2015, Trump attacked McCain, who had been held as a prisoner of war in Vietnam, as "not a war hero" and again criticised McCain after he died of brain cancer in August 2018.
"I was never a fan of John McCain and I will never be," Trump said earlier this year.
In one of his final public statements in July 2018, McCain blasted Trump's summit with Russian President Vladimir Putin as a "tragic mistake".
On Saturday, Klobuchar, who has previously touted her relationship with McCain while on the campaign trail, said an "arch of justice" started after Trump's "dark inauguration", CNN reported on Sunday.
"The path that we are on did not just start today. It didn't just start with the 2020 debates," she said. "The arch that we are on, this arch of justice started that day after that dark inauguration."
( With inputs from IANS )