Two women who have tested positive for Covid-19 got lost on their drive from Auckland to Wellington and required help - giving their helpers a "kiss and a cuddle", Parliament has been told.

National MP Michael Woodhouse claimed today that the pair, who travelled from London to New Zealand, had to meet someone for help with directions.

He said a source told him the two women were in a borrowed car and got lost on their way from Auckland to Wellington so stopped and asked someone for directions.

The women thanked their helper with a "kiss and a cuddle", Woodhouse claimed in the House.

Health Minister David Clark replied to Woodhouse's claim by saying he would be "deeply concerned" if that were the case as he had been assured the women had no contact with anyone during their journey.

Woodhouse: Who gave the women the car?

Speaking to reporters later, Woodhouse said: "Last night I received information from a reliable but confidential source that the story of an uninterrupted trip from Auckland to Wellington was not accurate."

The pair had become lost as they tried to leave Auckland, he reiterated.

"They called on some acquaintances for help with directions. When they were there, there was close physical contact, including a cuddle and a kiss.

"I'm calling on [Health] Minister to require the director general [of health Ashley Bloomfield] to look deeper into the circumstances of that journey, and reassure himself he's got all the facts."

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He said the source was "very reliable" and "closely connected".

But there was a time to protect sources, so he was not going to divulge who it was.

He said his information was reliable enough to ask questions about how they got their vehicle, which he said was borrowed, whether they stopped on the outskirts of Auckland, and whether they drove to Wellington without stopping for fuel or food or a toilet break.

It seemed unlikely that the women had driven from Auckland to Wellington without any comfort stops, he added.

He wasn't defaming anyone as he didn't know who the women were, he said.

The story that health chief Ashley Bloomfield had told may not be as it has been portrayed, he said.

He was not calling the women liars, he said, but he was asking the Health Ministry to dive deeper into whether the narrative that had been provided was accurate.

"I'm not saying anybody lied. I'm saying there needs to be a deeper analysis."

NZ First leader Winston Peters said if the claims were true, it would be "serious concerning", but if not, Woodhouse was playing "petty politics" and he should apologise.

When asked if heads should roll over the border failures, Peters said: "Of course – the three people who didn't do their job. They need to be found and they need to be held accountable."

He later said when asked which three people he meant: "Everyone needs to be held accountable, particularly on an issue to do with public safely like this."

He said neither David Clark nor Ashley Bloomfield should step down, and it was "plain ridiculous" to call for the head of a minister whenever something goes wrong in their ministry.