After a hectic cyber search, an intelligence officer said the origin of the electronic mails was traced on Tuesday to an Internet cafe in a middle-class neighbourhood of Lahore, where the New Zealanders will play their first match on November 29.
The e-mails, sent to New Zealand's embassy in Iran, its cricket board and the Pakistan Cricket Board, threatened New Zealand's players with death if they came to Pakistan.
Four players, Craig McMillan,
The tour was originally due to start on November 20, but has now been delayed until November 27.
The intelligence officer said authorities had interrogated the owner and an employee of the Internet cafe and prepared a sketch of the suspect based on the owner's description.
Police superintendent Mohammad Osman said the sketch had been distributed to other Internet cafes in case the suspect appeared, but no arrests had yet been made.