"Unfortunately, I have to keep this private for the moment," the 53-year-old told reporters at the meeting in Beverly Hills. "It's just one of those things, but thank you anyway."
Specifically asked by one member of the press, "The new baby. Were you as surprised by the news as we were?", Simon quipped, "I haven't read the newspapers. Am I missing something?"
Dressed in his signature white T-shirt, the savvy media star remained calm and collected in the face on immense pressure. He went on to say that he would open up about Lauren Silverman's pregnancy when the "time is right".
"There are a lot of things I will eventually clear up when the time is right," he explained. "I really have to be sensitive here because there are a lot of people's feelings involved."
Asked if he could reveal how he is feeling, Simon replied, "I would love to, but I have to respect a lot of other people's feelings."
The press conference came hours after it emerged that Lauren's husband Andrew has cited Simon in his divorce papers. He accuses his wife of adultery with Simon and of being "cruel and inhuman" towards him.
Andrew also released a statement. "My top priority is protecting my seven-year-old son while working to resolve all outstanding issues with my wife. Hopefully people can respect the interest of our child during this process."
In a separate statement, Lauren, 36, said, "I am committed to sorting things out with Andrew as amicably as possible to ensure the well-being of our son. I would hope for some space and privacy in order to work through this."
The pregnant brunette was all smiles as she stepped out in the Hamptons on Thursday with her son Adam, a tiny hint of a baby bump just visible. She later emerged in a tight black dress that clung to her burgeoning tummy.