The group Global Peace and Justice has sent her a letter asking her to withdraw from the tournament because of Israel's policies towards Palestinians.
Spokesman John Minto acknowledges they are asking Pe'er to make a significant sacrifice as she makes her living as a professional tennis player.
However he says greater sacrifices are being forced onto Palestinians.
The New Zealand protest group Global Peace and Justice earlier Tuesday said it had written to the 22-year-old Peer asking her to withdraw from the tournament "as a demonstration of your commitment to peace."
Global Peace and Justice also wrote to Peer and protested her presence at last year's tournament. The group said it opposes Israel's treatment of Palestinians and advocates a sports boycott of Israel.
The letter sent to Peer on Tuesday said her withdrawal from ASB Classic, a WTA Tour event, would be a "significant sacrifice."
Global Peace and Justice said sporting boycotts were "more visible than a trade or investment boycott and can have an important psychological impact. We saw this with the successful sports boycotts against apartheid [in] South Africa."
Pe'er has not responded to the letter but last year said she was disappointed to be singled out by protesters.
Protests against Israeli players is not new. Pe'er was subjected to a similar protest at last year's tournament, as well as a controversy at the 2009 Barclays Dubai Tennis Championships when the Dubai government refused to grant her a visa, preventing her from playing in the tournament. The men's Israeli Davis Cup team also suffered protests from anti-Israeli groups prior to their quarterfinal tie against Sweden, leading the Swedish tennis association to ban all spectators for the matches.
Stuff like this really makes me angry =/ She hits a fuzzy ball with a racquet, how is that hurting anyone? She doesn't control her government or what it does and she can't help where she was born. This is why politics and sports should not mix :(