"Their rights will be on my shoulders and I won't spare effort" to free them, he said.
Morsi is a study in contrasts: a strict Islamist educated in Southern California who vowed during his campaign to stand for women's rights yet argued for banning them from the presidency.
During the historic campaign, Morsi said he would support democracy, women's rights and peaceful relations with Israel if he won.
But he has also called Israeli leaders "vampires" and "killers."
Morsi focused his campaign on appealing to the broadest possible audience after a slogan associated with his campaign, "Islam is the solution," sparked concerns that he could introduce a fundamentalist Islamic theocracy.
During the campaign, he said he had no such plans. His party seeks "an executive branch that represents the people's true will and implements their public interests," Morsi told CNN's Christiane Amanpour.
Asked whether he would maintain Egypt's 1979 accord with Israel, Morsi said, "Yes, of course I will. I will respect it provided the other side keep it up and respect it."