The 70-year-old captain of Romania's Fed Cup team responded to the announcement that the world No 1 was pregnant with her first child by Reddit co-founder Alexis Ohanian by speculating about the colour of the baby's skin.
Speaking at a press conference, Nastase reportedly said: "Let's see what colour it has. Chocolate with milk?"
After being slammed by Williams, who said the comments were "racist", and becoming the subject of an investigation by the International Tennis Federation (ITF), Nastase apologised in a statement on Facebook, the AP news agency reported.
He was said to comment that he responded "spontaneously" upon hearing of Williams' pregnancy for the first time.
He added: "[Williams is] one of the greatest players of all times and I know how much work goes into achieving these results."
Referring to the incident during a Fed Cup match between Great Britain and Romania, in which Nastase reduced GB's Johanna Konta to tears after swearing at her, Nastase said his words were indefensible but that they came from a "desire to defend the interests of the Romanian team and Romanian tennis".
Nastase added that Konta should not have spoken with the chair umpire - a job reserved for the team captain.
He said: "I think what happened was exaggerated from all sides. Nonetheless, Johanna Konta should not have spoken with the chair umpire, that's what the team captain does."
Read the original article on Eurosport: Nastase apologises for 'spontaneous' Williams comments