Response from women MPs
"Eagle said she had been "patronised by better people than the prime minister", adding that Cameron should instead be apologising for the economy, which had "effectively flatlined for six months".
She told BBC News: "I don't think any modern man would have expressed himself in that way.
"The prime minister is responsible for what he says in the Commons. I think if there is an apology to make it should be for the dreadful growth figures we have seen today, which demonstrated that the economy has effectively flatlined for six months."
She said it was up to Cameron "as to whether he wants to annoy 51% of the population".
Labour's Caroline Flint accused Cameron of using the word "dear" to "put women down", and said she had been on the receiving end of the same tactic from the communities secretary, Eric Pickles, in the chamber last December, when he told her to "just get behind the programme then, dear".
Labour's deputy leader, Harriet Harman, said: "David Cameron's contemptuous response to Angela Eagle MP at prime minister's questions today shows his patronising and outdated attitude to women.
"Women in Britain in the 21st century do not expect to be told to 'calm down, dear' by their prime minister.""