Pakistan were on course to take a 2-0 lead in the three-day Asia/Oceania Group II tie on Friday when Sri Lankan referee Asitha Attygalla abandoned the contest due to an "unplayable court" in the neutral venue of Yangon, Myanmar.
As the encounter had been a designated 'home' tie for Pakistan, who are unable to host matches due to security concerns, Attygalla awarded victory to New Zealand.
An angry Qureshi questioned the referee's decision.
"I will meet with Davis Cup officials this week in London to tell them what actually happened in Myanmar and how we were treated unjustly by the referee," Qureshi told a news conference in his hometown Lahore on Wednesday.
"I think the referee was partial and favoured the New Zealanders."
Pakistan officials have already lodged an appeal with the International Tennis Federation (ITF), complaining that their players were left distraught and the team suffered financial loss due to the referee's decision.
Pakistan chose to 'host' the tie in Yangon after New Zealand refused to play in Pakistan due to security concerns.
New Zealand captain Alistair Hunt said on Friday the match had to be abandoned because a hole about "an inch deep and half a foot wide... opened up on the baseline, which proved too dangerous to play on".
Qureshi disagreed: "The area deemed dangerous was outside the lines of the court. I am convinced we were treated unfairly and unjustly and I want to plead this case for Pakistan."
The ITF confirmed it had received a complaint from Pakistan.
"The Davis Cup Committee will be considering both Pakistan's appeal and the report of the ITF referee (about the court being unplayable) in making their decision," an ITF spokesman said.
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