Jacinda Ardern said New Zealand could move to alert level 1 next week, which means all social distancing measures and curbs on mass gatherings will be lifted. Borders will remain closed, she said.

"Our strategy of go hard, go early has paid off... and in some cases, beyond expectations," Ardern said at a news conference.

The cabinet will decide on June 8, earlier than the planned date of June 22, she said.

New Zealand recorded no new cases of coronavirus for a 11th consecutive day on Tuesday, and has just one active case in the country.

This was largely because of a strict lockdown enforced for nearly seven weeks, in which most businesses were shut and everyone except essential workers had to stay at home.

"We will be one of the first countries in the world to return to this level of normality so quickly," Ardern said.

Thousands of New Zealanders marched on Monday decrying the death of George Floyd, a black American, in police custody in the US last week, despite social distancing restrictions.

Ardern said she was "horrified" by Floyd's death but noted that the protesters had flouted rules.

"I think I stand with everyone else in being horrified in what we've seen," regarding Floyd, Ardern told state broadcaster TVNZ in an interview earlier in the day.

"I don't want to stop peaceful protests... but rules are there to protect people," she said, adding that she understood the sentiment of the protesters.

Ardern has been described by some liberal supporters as an "anti-Trump," promoting issues such as social justice, multilateralism, and equality.