Lees-Galloway said he understood the applications were being made 10 at a time, and had asked for a briefing from Immigration NZ.
"This application was made under the settings we have inherited, and there's every likelihood they are legitimate applications and there is a genuine need. I need to make certain of that, and that's why I've asked Immigration NZ to brief me," he told Radio NZ.
He blamed the shortage of skills in the construction sector on the previous Government.
"I can understand why people are asking questions about why New Zealanders are not able to participate in this work. The previous Government failed to invest in the skills that New Zealanders need to participate in that sector."
Government policies including having a year of fees-free post-secondary education and the He Poutama Rangatahi employment scheme - $13 million to get 2000 young people into work in the regions - would help upskill the labour market, he said.
The Government also plans to introduce the KiwiBuild Visa to help build 100,000 affordable homes in 10 years. The visa would bring in up to 1500 foreign workers, conditional on taking on a local apprentice for each foreign worker.
"Where there are genuine skills shortages, and employers need to get workers and to use immigration to get workers, that's where we'll make sure the system works for them," Lees-Galloway said.
The latest unemployment figures, released yesterday, show the unemployment rate at 4.5 per cent, the lowest in nine years.
But underemployment - part-time workers who want to work more - rose to 6.3 per cent, the highest rate on record.
"There is capacity within the New Zealand labour market," said Lees-Galloway, who is also the Minister of Workplace Relations.
