Prime Minsiter John Key has reportedly expressed his regrets about Mr Brownlee's comments to Finland President Sauli Niinisto.
Finland's national broadcaster, YLE, reported that Mr Brownlee's comments came up in discussions between the Mr Key and the President when they met at the Nuclear Security Summit in Korea.
Commenting on his talks to Mr Key later, Mr Niinisto told media Finland was not the only country where unguarded comments were made.
"We decided to conclude the matter with an amusing tale that when I served as Finance Minister in Finland, many people wanted the New Zealand model," he said.
"This time round, people in New Zealand looked to the Finnish model. Perhaps together they might form a perfect model."
Meanwhile Mr Brownlee has also apologised for disparaging remarks about Finland, when he described Finns as uneducated, unemployed murderers who don't respect women.
The storm started over comments Mr Brownlee made in Parliament last week in response to Labour leader David Shearer's speech calling for New Zealand to follow in Finland's footsteps.
Finnish media picked up the story and said Mr Brownlee caused embarrassment to their country, while a Facebook page has also been set up calling for him to travel to Finland to "learn some facts".
Finnish comedian Tuomas Enbuske has lashed out at Mr Brownlee in his popular show, making comments about Brownlee's weight as well as the sheep population in New Zealand.
Speaking to reporters this morning, Mr Brownlee apologised to anyone who was offended by his comments, but said they were made in good humour.
"I'm sure that New Zealanders have been the butt of all sorts of jokes at various times and not taken offence at such a thing," he said.
"If I've offended people, I'm sorry about that, all I can say it was meant to be humorous and I apologise for people not seeing the humour in it."
Showing off his Nokia phone, Mr Brownlee said he carried "a little bit of Finland with me all the time".
"Wonderful country, very clever, we do like their mixed-ownership model and lots about them."
But Labour deputy leader Grant Robertson did not appear as amused by the matter, and said Mr Brownlee should have apologised.
"It's an embarrassment for New Zealand. Finnish television's got a hold of it now, I think it's a situation where Gerry needs to realise that he said something silly and embarrassing and he should just apologise."
In Parliament last week Mr Shearer said the Finns had managed to transform their economy "through innovation and talent".
In response, Mr Brownlee, who is Leader of the House, said: "I think we need to understand a few things about Finland.
"It's unbelievable isn't it. That you'd ... make a speech saying I want New Zealand to be like Finland which has worse unemployment than us, can hardly feed the people who live there, has a terrible homicide rate, hardly educates their people and has no respect for women."
Over the weekend, his comments made headlines in the Nordic nation with one news site saying Mr Brownlee sneered the remarks.
Minister-Counsellor Juha Parikka from the Finnish Embassy in Canberra, which is accredited to New Zealand, said Finland intended to examine Mr Brownlee's comments carefully. Ms Parikka told Helsingin Sanomat that her interpretation was that it was just a "domestic political torque in New Zealand" and colourful language was more common in the New Zealand Parliament.
"It is very different from that which Finland has become accustomed to."
She said that New Zealanders and Finns understood each other very well because the two countries were of the same size with similar problems.
"My guess is that New Zealanders will be very sorry," Ms Parikka said.
The deputy head of mission at the Finnish Embassy in Canberra has written to the Ministry of Foreign Affairs and Trade seeking an explanation, saying he wants to know if there will be any reaction from the Government, Radio New Zealand reported.
Meanwhile, Mr Brownlee's comments have also upset Finns living in New Zealand and a Facebook page has been set up calling for him to go to the country to "learn some facts".
Merja Myllylahti, a Finnish lecturer at Auckland's University of Technology, created the group so people had an outlet to "politely discuss" Mr Brownlee's knowledge about Finland and share facts about the Finnish education system, gender equality and welfare of its people. Last night the page had more than 150 members.
According to the OECD Better Life Index, Finland's murder rate is nearly twice that of New Zealand. It also has worse unemployment and health provision.
But on economic indicators such as income and work-life balance, Finland is ahead of us - and for education is rated best in the world. Its GDP is also rising faster than New Zealand's.