During a radio interview, Cruz was asked whether changing a baby's diapers was a wife's job, to which he said: "It's a parent's job. I can tell you with our girls, I changed a lot of diapers. Heidi changed a lot of diapers," Cruz said.
Cruz, who is married to Heidi Nelson, said that when a diaper needs changing, whoever's closet jumps on the grenade.
Cruz's statements came after Trump said that changing baby's diapers were a wife's job. When asked whether he (Trump) has ever changed diapers, Trump said: "No I don't do that."
Trump went on to add, "There's a lot of women out there that demand that the husband act like the wife and you know there's a lot of husbands that listen to that."
Meanwhile, Trump on Wednesday declared himself the "presumptive" Republican nominee after sweeping the five primaries in north-eastern states.
"I consider myself presumptive nominee," Trump said in his victory-speech after winning the nominating contests in Connecticut, Delaware, Maryland, Pennsylvania and Rhode Island.