"Throughout that contribution, the member referred to the Hon Paul Goldsmith as Goldstein. I don't want to suppose that that was a slur, potentially an ethnic slur to those of the Jewish faith who share the name Goldstein," Willis said.
Mitchell also referred to Goldsmith as Goldstein during a debate in June.
"Thank you, Madam Chair. I appreciate the call this evening. A great contribution there by the member Mr Goldstein and I have to also say that the one thing that he forgot to say in his contribution was that he did support the bill, and for all the right reasons."
He apologised at the time, saying it was a slip and not deliberate.
Hutt Valley National MP Chris Bishop, who was also upset at Mitchell's comments, posted video of the incidents on his Facebook page.
Mitchell said today it was "cheeky banter, nothing more" and a reference to the bumbling Ira Goldstein from the ASB ads which ran from 1999 to 2010.
"Goldstein was a bit of a buffoon, and it was a reference to [Goldsmith's] buffoonery. It was certainly not anti-Semitic."
Mitchell said it was not intended as an insult and he got on very well with Goldsmith.
"The amount of insults that get thrown across the House on a regular basis towards our party and our leadership. We don't take any offence to it, we just shrug off, it's just the nature of the House.
"I think [Willis] is being a little bit precious. Anyone that's taken an offence to it like Nicola Willis has is being a little bit over-sensitive," Mitchell said.
Goldsmith, who is based in Epsom which is home to a synagogue and a strong Jewish community, said he would give Mitchell the benefit of the doubt and assume it was a reference to the ASB ads.
NZ Jewish Council spokeswoman Juliet Moses said it was disappointing to see a Member of Parliament resorting to anti-Jewish stereotypes.
"We expect more of our MPs. We appreciate the comments made by Nicola Willis, and the Speaker, calling out those statements. Such racism is unacceptable anywhere, but particularly in our House of Parliament by elected officials," Moses said.