Qureshi, 33, the country's first player to reach a Grand Slam doubles final, was part of the squad that faced New Zealand in an Asia Oceania group II tie, which was shifted to Myanmar over security fears in Pakistan.
Pakistan were leading 1-0 on Friday and Qureshi was ahead in the second singles match when Sri Lankan referee Ashita Ajigala stopped the match and awarded the tie to New Zealand, as the courts were Pakistan's responsibility.
The Pakistan Tennis Federation had already announced it was lodging a protest with the International Tennis Federation (ITF), but Qureshi said he would meet Davis Cup officials in London to present the team's case.
"I am leaving for London and will meet Davis Cup officials on Friday to put Pakistan's case before them and I am positive of a solution as the tie was unfairly awarded against us," Qureshi told a press conference.
"It seemed the referee was not working for the ITF but for New Zealand and he was clearly partial and unjust."
The area declared unplayable was outside the lines of the court, he added.
Qureshi paired with India's Rohan Bopanna, dubbed the "Indo-Pak express", to reach the final of US Open doubles in 2010, where they lost to the American Bryan brothers.
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