"We will not play the two Tests and five one-day internationals in New Zealand if they don't keep their commitment (here)," Pakistan Cricket Board (PCB) chairman Tauqir Zia said.
New Zealand Cricket (NZC) said it would decide by Monday if its players would go to Pakistan for the five one-day internationals after receiving an e-mail threat from unknown sources.
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NZC said it was looking into concerns about security and safety of its players in Pakistan.
Zia said that Pakistan had given all assurances of security and safety to New Zealand.
"Bangladesh and South Africa have completed successful tours of Pakistan without any problems. So we are not ready to accept any New Zealand cancellation," he said.
"Pakistan cricket can't be expected to survive like this. We can't have teams refusing to tour Pakistan because of perceived threats to them."
"We are not prepared to accept that a tour is cancelled because of a unnamed e-mail threat. But we are also seriously investigating the threat through our sources."
Pakistan are scheduled to visit New Zealand in December-January.
New Zealand are due to arrive in Islamabad on November 20 to play one-dayers in Faisalabad, Rawalpindi and Karachi.