Ardern said Cabinet had today discussed the alert level decision-making processes.
Ministers would fully review the alert levels next Monday, she said.
If there were no further cases in the coming days, New Zealand could be in a position to move to alert level 1 next week. More details on what alert level 1 would look like would come this week.
So far the tail or spike of Covid-19 hadn't eventuated and there was increasing optimism it wouldn't happen.
"Our strategy of going hard and early has paid off."
But authorities needed to see if more cases came through after relaxing restrictions to mass gatherings to 100 on Friday.
Lack of physical distancing at yesterday's marches
Ardern said it wasn't up to the Government to decide whether police should have enforced the level 2 distancing requirements at the Black Lives Matter protests in this country yesterday.
Cabinet did not decide to move to alert level 1 today because it was a "balanced decision" based on health and economic advice and the country had only relaxed the restrictions on mass gatherings last week, Ardern said.
She confirmed that Deputy Prime Minister Winston Peters had expressed his thoughts on moving to alert level 1 both publicly and privately.
The Cabinet decision today to leave the decision on moving until next week was a consensus decision but Ardern said there was an alternative view presented.
Ardern said sliding backwards in alert levels would be the worst thing possible for the country.
Director-general of health Dr Ashley Bloomfield had not changed his views on the 100-person limit for mass gatherings, Ardern said, despite not recommending that yesterday's protesters should self-isolate.
New Zealanders were "for the most part" experiencing a relatively normal life at the current restrictions, with the economy roughly down by 5 per cent, she said.
The 50+ Avatar film crew members who arrived in New Zealand on Sunday were now quarantined at a "government-approved" hotel and paid for their own costs.
About 150 people had been granted permission to enter the country for economic reasons, Ardern said.
Trades training programme
Ardern was joined by Education Minister Chris Hipkins for the post-Cabinet press conference to give more details about the free trades training programme announced in the Budget.
Ardern said unfortunately the economic damage of the virus was something every country was experiencing but the Government could ensure no one was left behind.
The Targeted Training and Apprenticeships Fund was an "important part of the overall plan".
It would mean any form of apprenticeship would be free from July 1 this year, which should encourage businesses to take on apprentices.
Hipkins said many New Zealanders would be looking to re-train as a result of Covid-19.
The package was designed for all learners, not just school leavers, he said.
The initial areas would be refined next year when there was more understanding about how Covid-19 had impacted the labour market, Hipkins said.
Ardern earlier on NZ marchers
Earlier today Ardern had strengthened her criticism of the Black Lives Matter protests, saying "it was not right" and the rules were there for a reason.
"They have breached the rules. It was not right. New Zealanders have given up a lot and I need to keep asking the team of five million to stay together so we can reach the finish line. I understand the sentiment but I cannot condone the breaking of the rules."
Ardern said the decision on whether the protest organisers should be prosecuted lay with police as the Government didn't intervene with enforcement.
She was asked why the Ministry of Health and the police didn't put out notices advising against the gatherings.
She said "we have all put out the message, don't gather - it is not a good idea".
Alert level 1
New Zealand was in a position to consider to moving to level 1 earlier than expected because of the success of the lockdown.
At alert level 1, the border restrictions would remain in place with intensive testing and physical distancing encouraged, but there's no limits on gatherings.
"Level 1 potentially means we keep our border restrictions, but life feels very, very normal otherwise."
Ardern said Cabinet considering the move to level 1 early wasn't a result of Deputy Prime Minister Winston Peters' pressure, rather a result of the encouraging evidence.
