We offer our deep condolences to his son John and the entire family.

I must offer my condolences, even though she might not want to hear them.

He was one of the few people who had called up to offer her condolences.

We offer our condolences to her family and many friends.

Other than to offer my condolences, I didn't speak much with her.

"We would like to thank the people who have already offered their condolences."

Sure, people came up to me and offered their condolences.

Then perhaps someone else should attack them, and you will offer condolences?

"I just came to offer them my condolences on their son's death."

She offered him her condolences, and a few days later they had dinner together.