Foreign Affairs Minister Murray McCully is standing by official advice that there was no basis to take up any concerns with the Israeli government over the activities of its nationals after the Christchurch quake.
On Wednesday, John Key confirmed inquiries were made into the activities of a group of Israelis who were in Christchurch at the time of the 22 February quake.
The inquiries found no evidence to suggest there was a link between the group and Israeli intelligence.
Mr McCully says they don't know all the facts but a number of factors made it prudent to make inquiries,such as the pressure being placed to give access to the quake red zone to an Israeli search team.
Three Israelis died in the 22 February earthquake. One of those killed, Ofer Binyamin Mizrahi, died in a van, and three others who had been in the same vehicle quickly left New Zealand.
Mr McCully says a report that Mr Mizrahi was found with five passports is incorrect and that checks have shown no-one hacked into any police computers, nor any other computers that would cause concern.
Southland Times editor Fred Tulet is standing by his report that the Security Intelligence Service (SIS) is auditing the police national computer because of concerns that Israeli forensic scientists in the city after the quake could have embedded malicious software to get security intelligence information.
Search team was legitimate, says father
Israeli citizen Gabi Ingel was one of three Israelis who died in the February earthquake, but was not one of those who were the subject of inquiries.
His father, Gil Ingel, says he sent a search and rescue team to New Zealand.
Mr Ingel says he was desperate to find his son alive and sent the rescuers because of concerns about the competence of recovery operations in the city.
"I understood that the Israeli government extended its proposal to New Zealand to send an official group to help in the rescue effort and was refused, so I gathered a group of people that are expert in that field," he said.
Israel-NZ relations 'very good'
Israel's Ambassador to New Zealand, Shemi Tzur, arrived back in the country on Wednesday, telling waiting media that relations between the two countries were very good.
The Israeli government says its satisfied with the processes carried out by the New Zealand Government does not need to take the matter further.
Meanwhile, Wellington Regional Jewish Council chairman David Zwartz says he's disgusted that Mr Mizrahi has been caught up in a spy scandal.