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"Maybe it is the case that Donald, there have been multiple media reports about Donald's business dealings with the mob, with the mafia," Cruz said on "Meet the Press."
"Maybe his taxes show those business dealings are a lot more extensive than has been reported," he added.
Cruz repeated the suggestion on ABC's "This Week," seemingly stunning host George Stephanopoulos.
"Business dealings with the mafia?" Stephanopoulos asked, incredulously.
When pressed, Cruz cited news reports that have investigated Trump's alleged ties to New York and Philadelphia crime families decades ago. He specifically named S&A Construction, which was controlled by Anthony "Fat Tony" Salerno and Paul Castellano, who headed two New York crime families, according to CNN.
"ABC, CNN, multiple news reports have reported about his some dealings with, for example, S&A Construction, which was owned by 'Fat Tony' Salerno, who is a mobster who is in jail. It is owned by two of the major New York crime families," Cruz said.
According to CNN, S&A Construction built Trump Plaza condos.
Trump has faced extensive scrutiny over his tax returns in the past week. Mitt Romney, the 2012 Republican nominee, openly questioned earlier in the week whether Trump's returns might contain a "bombshell."
"Well, I think there's something there. Either he's not anywhere near as wealthy as he says he is, or he hasn't been paying the kind of taxes we would expect him to pay. Or perhaps he hasn't been giving money to the vets or the disabled, like he's been telling us he's been doing," Romney said.
Cruz and another Trump rival, Sen. Marco Rubio of Florida, both released partial tax returns Saturday evening in an attempt to put more pressure on Trump.
For his part, Trump has said he plans to release his returns. But he said he would wait until a federal audit was complete.
"Look, let me just tell you something. Let me just tell you something. I want to release my tax returns but I can't release it while I'm under an audit. We're under a routine audit. I've had it for years. I get audited," Trump said during the Thursday-night Republican presidential debate.
"And obviously if I'm being audited, I'm not going to release a return," he added. "As soon as the audit is done, I love it."
Watch Cruz's speculation on 'This Week' below:
WATCH: @TedCruz speculates Donald Trump's taxes could show mafia ties https://t.co/z5nCcdKik2 #ThisWeek https://t.co/uVI88dx8pe