"Everybody knows John McCain is going to endorse Marco Rubio," Cruz told reporters Thursday when asked about how the Arizona senator had brought up whether his birthplace would make him ineligible for running for president.
"Their foreign policies are almost identical. Their immigration policies are identical," Cruz said. "So it's no surprise that people who are supporting other candidates in this race are going to jump on the silly Attacks that occur as we get closer and closer to the election."
Rubio has earned more establishment Republican support than Cruz, but McCain has not endorsed the Florida senator in the 2016 GOP presidential race -- instead holding off on supporting another candidate after his preference, South Carolina Sen. Lindsey Graham, dropped out.
Early Thursday evening, a McCain spokeswoman said he will not be endorsing a primary candidate at this point in the race.
Cruz's comments come after McCain said it's "worth looking into" whether the Texas senator is eligible to run for president, since he was born in Canada.
In an interview Wednesday on Phoenix CBS affiliate KFYI
, McCain said the questions raised by Republican presidential front-runner Donald Trump over Cruz's eligibility are legitimate.
"I think there is a question. I'm not a constitutional scholar on that, but I think it's worth looking into. I don't think it's illegitimate to look into it," McCain said.
On Thursday, Trump again hit Cruz and referenced McCain's comments.
"It was a very wise move that Ted Cruz renounced his Canadian citizenship 18 months ago. Senator John McCain is certainly no friend of Ted!," Trump tweeted.
McCain has relished taking occasional shots at Cruz. The two have never been friendly -- with McCain once describing Cruz and his allies as the Senate's "wacko birds."
McCain himself was born outside the U.S. mainland, in the Panama Canal Zone -- a military base where his father was then stationed.
Another Arizona senator, 1964 Republican presidential nominee Barry Goldwater, had set the precedent when the Supreme Court ruled him a natural-born citizen and therefore eligible under the Constitution for the presidency even though he was born in pre-state Arizona when it was still a territory.
Asked if Cruz should get ahead of the issue, McCain said: "I would think so."
"I got ahead of it on being born in the Canal Zone when I was running in 2008," he said. "I said, 'Look, there is a precedent set: Barry Goldwater ran for president; was born in Arizona when it was a territory.' The Panama Canal was a territory of the United States of America."
McCain also said he sees the Republican presidential nominating contest as far from settled.
"We live in most interesting times, and I do believe that there are going to be a lot more surprises, because every pollster I've talked to said there are still a lot of people who have not made up their minds," he said.
On Thursday, Cruz also dismissed Donald Trump's suggestion that he ask a judge for a declaratory judgment to stave off any sort of legal challenge to his candidacy.
"No," Cruz said, "it's not anything that's going to happen and I'm not going to be taking legal advice anytime soon from Donald Trump."