After his comments were published, Calderoli said "if I've offended her, I apologize."
"It was a joke, a comment in a joking way. There was nothing particularly against her," he said. "It was just my impression. ... It is all very well that she be a minister but in her own country. Given that this government needs to govern Italy, I hope that it is done by Italians."
Kyenge responded diplomatically, saying Calderoli "does not need to ask forgiveness to me, but he should rather reflect on the political and institutional role that he carries. It is on this that he needs to make a profound reflection also to then apologize."
She added, "Also, he must go beyond putting everything on a personal level. I think the time has come for us to study the problem of communication."
Kyenge has also received death threats before visiting an area where the Northern League is powerful.
A local politician recently said on Facebook that Kyenge should be raped so she can understand the pain felt by victims of crime, which some politicians blame on immigrants.
She's been called a "Congolese monkey," "Zulu" and "the black anti-Italian." One Northern League official said "she seems like a great housekeeper" but "not a government minister."
Italian Prime Minister Enrico Letta appealed to Northern League leader Roberto Maroni to "close this chapter right away."
Tensions over immigrants
Italy has been experiencing its highest level of unemployment in more than 20 years.
In tough times, some Italians focus their anger on immigrants, Mazzuca, the newspaper editor, told CNN.
"The economic crisis is worsening the situation," he said. "Jobs that until a few years ago wouldn't have even been considered by Italians are now becoming precious."
There have recently been more and more reports of Italians beating foreigners, particularly street vendors, Mazzuca said.
He said doesn't believe that Italians generally are racists and hopes Kyenge will be able to ease racial tensions.
"I really think that Kyenge is the right person in the right place," he said. "As an eye doctor, she is able to see in the distance."