"There's two criminal investigations under way but I can't talk about the details. What I can say is that if matters are upheld that are criminal or outside our values or standards, people do not get graduated," Fraser told Radio New Zealand.
Among the allegations against the four recruits are indecent assault, careless driving and intimidation.
Another six recruits involved in a drinking incident at the Royal New Zealand Police College were told off and still graduated earlier this month.
Fraser said today it was a "very, very minor matter".
"They were noisy in the barracks and were up late at night doing some very silly things."
The 100 recruits in Wing 318 was the largest intake by the Police College in 12 years.
Nash agreed it was "not a great look" but said there were two sides to every story. Police had investigated claims against a recruit accused of harassing his girlfriend's brother who then went on to win the Minister's Award as top graduate last month.
"Police investigated this and found insufficient evidence … Police determined that this chap hadn't done anything that warranted any charges against him," Nash told RNZ.
Nash said he "completely refuted" a suggestion that people who previously may not have been accepted into training were now getting through as a result of the coalition Government's promise to boost police numbers.
"The men and women who are applying to be police officers now are of a high quality, keeping in mind that 75 per cent who applied didn't get through."
National's police spokesman Chris Bishop said the Government's plans to introduce 1800 new police officers within three years was to blame for the lower standard of officers.
Recruits were being pushed through even if they were unsuitable and it had resulted in declining behaviour and ethical standards among new recruits, he said.
Other police officers had also raised concerns about the declining standards with him.
"These officers have to serve with the people coming through," Bishop said. "They are worried that the force's overall service to the public will decline."