"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 and two-time Grand Slam winner, 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 a child.
"My life remains dedicated to tennis and its audiences, so please accept my apologies, for whatever they may be worth right now."
The day after the Williams comments, Nastase was kicked out of a Fed Cup tie between Romania and Britain after swearing at the umpire, at Britain's pregnant captain Anne Keothavong and at their number one player Johanna Konta.
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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.
"I was 5 when I first picked up a racket. 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 new 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.
"Joanna 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.