Sen. Ted Cruz, R-Texas,  on Tuesday refused to say whether he would deport a family of undocumented immigrants with U.S.-born children and instead accused Fox News anchor Megyn Kelly of posing a "liberal journalist" question.

"If you have a husband and wife who are illegal immigrants, and they have two children here who are American citizens -- would you deport all of them?" Kelly asked the Republican presidential hopeful. "Would you deport the American citizen children?"

"Megyn, I get that that's the question you want to ask," Cruz replied. "That's also the question every mainstream media liberal journalist wants to ask. They focus exclusively on 12 million people."

He then offered an explanation of how he thinks the immigration system should be changed, suggesting a need for a bipartisan deal on border security and streamlined legal immigration, the Washington Post noted.

Kelly, for her part, proceeded to invoke GOP frontrunner Donald Trump, who had attacked her aggressively after she questioned his history of offensive statements about women during this month's Republican presidential debate -- but who was not been shy about voicing his views on the proposed deportation of undocumented immigrants.

"That doesn't sound like an answer," the Fox News host challenged Cruz. "Mr. Trump answered that question explicitly last night on 'The O'Reilly Factor.' Will you do so now?"

The senator continued to refuse, arguing that Kelly's inquiry was a "distraction."

"We actually (need to) solve the problem," Cruz said. "You know it's also the question Barack Obama wants to focus on."

Trump, meanwhile, had told Fox News commentator Bill O'Reilly, "We have no choice" but to deport a Los Angeles couple of undocumented immigrants with two citizen children -- a hypothetical scenario offered by the pundit, Mediaite recalled.

The U.S. immigration system was "totally out of control," the real-estate tycoon turned presidential candidate argued, adding that many immigrants would subsequently be able to return to the country by applying for residency from abroad.