WELLINGTON - More threats were made against New Zealand schools Thursday a day after bomb hoax calls -- possibly from overseas -- disrupted six schools.

The New Zealand Police said Thursday that staff were responding to further incidents involving calls "of a concerning nature" made to an unspecified number of schools.

Police and school staff were searching the schools, said a New Zealand Police statement.

"Today's calls may be linked to the events of yesterday, where calls were made to six schools around the country," said the statement.

"These calls were of an automated nature and our initial inquiries suggest that they may have originated from overseas."

Police searched six schools -- four in the North Island and two in the South Island -- before giving them the all-clear, Superintendent Chris Scahill said in a statement on Wednesday.

Each call had stated an explosive device had been left on site.

Police were aware of "very similar incidents" occurring abroad, including in Australia and the United States, in which recorded voice messages were directed at schools.

New Zealand Police were liaising with law enforcement agencies overseas in their investigation, said Scahill.