Mr Mark made the comment during a debate on Tuesday on law changes to amend shop trading hours at Easter.
Ms Lee, who was not in the House at the time, had earlier said she was surprised that shops were forced to close.
Mr Mark accused the National MP of condescending behaviour and said: "Well I have got a short message, if you do not like New Zealand go back to Korea."
Act Party leader David Seymour raised the issue in the House this afternoon, saying that the New Zealand First MP should apologise.
At the time of the comment, Justice Minister Amy Adams immediately accused him of racism.
"Racism and vitriol," she said.
Ms Lee is a New Zealand citizen and moved to New Zealand from Korea 30 years ago.
On the same day, Mr Mark was ordered to leave the House after repeatedly challenging the Speaker David Carter.
During the debate, Ms Lee said: "Sometimes, as a migrant … it used to really surprise me, having grown up overseas and come to New Zealand, to see New Zealand shut down at a particular hour.
"That was really, really surprising. You know, we were closing shops at 5 o'clock when in other countries shops were open to 10 or midnight, or all night."
Mr Mark defended his response on the way into Parliament today.
"I object to being told we need to grow up. Some people who come here might think we're a bit antiquated or a bit silly.
"Maybe they do think we need to grow up. But they've got two choices, they can move on."
When reporters pointed out that Ms Lee was a New Zealand citizen, Mr Mark said: "Fine, but you know, a lot of people resent being told to grow up."
He added: "If people want to … challenge some of our fundamental beliefs, then they can expect a robust [response]."
Asked whether he was a racist, Mr Mark said that Assistant Speaker Lindsay Tisch did not rule that his comments were racist.
At the time, Mr Tisch called for order and said: "This is a robust debate and we will just ask you to calm things down."
No MPs made a complaint or a point of order.
MPs from across the House criticised Mr Mark's comments this afternoon.
Mr Seymour said: "Normally we give Ron Mark a bit of a leash because he's not the brightest bulb in the tree. But this sort of racism is not acceptable."
He said the remarks were "absolutely disgraceful" and "an embarrassment to New Zealanders".
Mr Seymour said the New Zealand First MP should be made to withdraw his comment in Parliament and apologise to Ms Lee.
United Future leader Peter Dunne said the comment was "appalling" and that there was no place "for that sort of racism under any circumstances".
Mr Mark's colleagues defended their deputy leader.
New Zealand First MP Barbara Stewart said he was not racist and his comment was "taken out of context".
Another MP, Pita Paraone, said he had heard "more vitriolic" comments made by MPs in the past.
"I didn't think it was a racist comment. I think it was said in the heat of the moment as part of the theatre of Parliament."
New Zealand First leader Winston Peters defended his deputy leader this afternoon.
Any claims of racism were "poppycock", he told the Herald.
"If someone is complaining about the country they're in, they have always got an option.
"It's one of the great freedoms we have in this country. They can always go back home. Unlike some of the places they've come from."
"If you've lived here for 30 years why would you keep complaining about it when the greatest part of your life in terms of age and experience has been expended in New Zealand?"
He added: "Frankly, I'm sick and tired of the people who come to this country, ignore our values, our laws, and pine for a past, whether they come from the UK or from Asia or anywhere else that does not belong here."
Mr Peters said there was no need to speak to Mr Mark about the issue and no action would be taken
- By Isaac Davison of the New Zealand Herald
