Pakistan has objected to Tennis New Zealand's request for a neutral venue for their Davis Cup tie in July.
Tennis New Zealand contacted the International Tennis Federation, asking for the tie to be moved out of Pakistan, citing security concerns.
But the Pakistan Tennis Federation says New Zealand should either play in Pakistan or be fined for refusing to.
The ITF fined Australia 15 thousand dollars last year for refusing to play in India because of security reservations.
Tennis New Zealand has written to the International Tennis Federation wanting the tie shifted.
New Zealand is the latest country to have reservations about participating in sports events in Pakistan, following the terrorist attack on the Sri Lankan cricket team in Lahore in March 2009.
It lost it's co-hosting status in the 2011 Cricket World Cup and had to move the home cricket tour against Australia and New Zealand to the United Arab Emirates.
Pakistan played their last three Davis Cup opponents, Oman, Hong Kong, and the Philippines, away from home due to those teams' reservations about playing there.
The International Tennis Federation is yet to comment.