Only about 50 people booked to fly on Air New Zealand's ATR fleet today will not be able to do so, the airline says.

The airline's 11-strong ATR72-500 fleet, operated by Mount Cook Airlines, was grounded for safety inspections on Sunday after hairline cracks were found around the cockpit windows of one aircraft.

The ATRs were gradually being brought back into service, with four flying today and nine expected to be back in the air by the end of the weekend, an Air NZ spokeswoman said.

One was awaiting a part and another was undergoing planned maintenance.

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Today, all but 50 of the airline's expected 4000 travellers would be able to fly, she said.