Upon learning of Williams' pregnancy last week, the 70-year-old Nastase said, "Let's see what color it has. Chocolate with milk?"
The 35-year-old Williams, who got engaged to Reddit co-founder Alexis Ohanian in December, is black and her fiance is white.
Nastase, who earned the nickname "Nasty" for his on-court outbursts in the 1970s, said his reaction was "spontaneous."
"At the press conference I was asked what opinion I had about Serena being pregnant," said Nastase, who is the captain of Romania's Fed Cup team. "I then found out for the first time (she was pregnant) and my reaction was spontaneous."
The day after his comments about Williams, Nastase was kicked out of a Fed Cup match for verbally abusing Johanna Konta and British captain Anne Keothavong during Konta's Fed Cup match against Romania's Sorana Cirstea last Saturday.
Romania won the best-of-five series 3-2, but Nastase was banned by the International Tennis Federation.
"I am fully aware that nothing can truly excuse my statements -- not the tension of a high-stakes game, not my traditionally irreverent attitude, not the unfortunate escalation of the situation," said Nastase, a two-time Grand Slam winner and former No. 1 player.
"My life remains dedicated to tennis and its audiences, so please accept my apologies, for whatever they may be worth right now."
Earlier this week Williams posted a statement on her Instagram account explaining her disappointment with Nastase.
"It disappoints me to know we live in a society where people like Ilie Nastase can make such racist comments towards myself and unborn child, and sexist comments against my peers," Williams wrote. "I have said it once and I'll say it again, this world has come so far but yet we have so much further to go. This or anything else will not stop me from pouring love, light and positivity into everything that I do. I will continue to take a lead and stand up for what's right."