"She is a formidable woman, she's brilliant, she's hardworking," Sanders said of Hillary Clinton on CNN's "Wolf."

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"We just differ on ideas and solutions for the future. But to demean her that way it's just not acceptable," Sanders continued.

"It certainly doesn't square with his comment that 'nobody cherishes woman more than I do.' My husband cherishes woman more than he does and he [Sanders] respects women as well, and it seems that that's a real problem with Donald Trump," Jane Sanders said.

Clinton and Trump have been exchanging jabs for days over the gender-based critique, with Trump doubling down on his attack while Clinton has knocked him for suggesting she was "shouting."

On the Democratic race, Jane Sanders insisted Thursday that her husband would continue in the race through the California primary June 7 and to the Democratic convention in July, despite Clinton winning the necessary delegates putting her on the verge of clinching the nomination.

Sanders has pushed to have a role in forming the party's agenda this summer.

"One of the reasons to stay in – even if the math looks worse going down the line – is to make sure than everybody has the opportunity to vote for the candidate of their choice and to express their opinion about the agenda that they want the country to move forward with, and we're doing that," she said.