He did however have another pop at Britain's number one women's player Johanna Konta, who was left in tears during last weekend's combustible Fed Cup tie with Romania, and said his behaviour "has been exaggerated by all".
"My words during the Fed Cup have rightfully caused controversy and upset the audience, the press and, most painfully for me, the tennis world," the former world number one, 70, said on Facebook.
He said that his comments last Friday about the pregnant Williams - he was overheard by a journalist talking about her baby being "chocolate with milk" – was a "spontaneous" reaction to hearing she was expecting her first child.
"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," he said.
"My life remains dedicated to tennis and its audiences, so please accept my apologies, for whatever they may be worth right now."
The comments last Friday prompted outrage from Williams, the 23-time Grand Slam winner, and messages of support from the world of tennis and beyond.
"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, 35, had said.
The day after, Romanian Fed Cup captain Nastase was kicked out of the tie with Britain in Constanta after swearing at the umpire, at Britain's captain Anne Keothavong and at an upset Konta.
Nastase, a two-time Grand Slam winner, also reportedly propositioned the married and pregnant Keothavong.
Nastase, renowned during his golden era for his pranks, hot-headed unpredictability and being a playboy, ignored the ban on Sunday and turned up at the venue on the Black Sea coast. He was seen by reporters walking into the VIP lounge.
The ITF later confirmed Nastase was not allowed to be on site in any capacity and the Romanian Tennis Federation president subsequently said he had left.
"I was five when I first picked up a racquet. Since then, tennis has been more than a sport or a profession for me. Tennis has been, and is, my life, and for tennis I have sacrificed almost everything, personal or professional," Nastase said in his statement.
"Unfortunately, now, in my 70s, I have somehow managed to do something I have never wanted or even imagined: to feel tennis moving further away from me. The last few days have been difficult for me," he said.
Nastase took another shot however at Konta, who broke down in tears after abuse from Nastase – leading to the Fed Cup tie to be temporarily suspended – and left the court.
Romania went on to win the tie 3-2 the next day.
Konta "had no right to speak to the chairman, the team captain is the only one who can do this. I asked the chairman for some explanations in a civilised manner, but he sent me to the stand", he said.
"In the stand they withdrew my status as captain of the Romanian team and I became a simple spectator. After this, the referee suspended the match.
"I do not understand why he did it and based on what point from the regulation?"