Tennis Australia faced fierce criticism after a player retired with breathing difficulties in the opening round of qualifying matches for the Australian Open.
Jakupovic was leading her Round 1 Open qualifying match against Switzerland's Stefanie Voegele when she collapsed to her knees with a coughing fit.
Other top players, including former world number one Maria Sharapova, were preparing for the year's first Grand Slam at the warmup Kooyong Classic on Tuesday in Melbourne's eastern suburbs where air quality was rated "very poor".
At the Kooyong Classic, in the Melbourne suburbs, players and officials chose to stop play between Maria Sharapova and Laura Siegemund at 5-5 in the second set due to the smoke.
Siegemund had taken the first set 7-6, with the pair locked at 5-5 in the second when play was called off.
"Both players are feeling the smoke so we are going to stop the match at this point", the umpire said.
Air pollution was at hazardous levels across the city due to thick bushfire smoke, and people are being told not to go outside.
It's an obvious concern with the world's eyes set to be glued on Melbourne during the two-week championship from Monday when thousands of worldwide and Australian tennis fans will also throng to the precinct.
"During the period of when we suspended practice and restarted the matches there was an improvement in the conditions".
Organisers said further decisions on match scheduling would be made using onsite data and in close consultation with its medical team, the Bureau of Meteorology, and scientists from the Environmental Protection Agency in Victoria state.
"We have access to real-time monitoring of air quality at all of our venues and are working closely with medical personnel and local experts onsite to ensure we have the best possible information available to make any decisions regarding whether play should be halted at any point".
Tennis Australia's chief operating officer Tom Larner said they would be treating any smoke stoppages in the same way as an extreme heat or rain delay.
Earlier on Tuesday, the EPA's website crashed after receiving a "significant amount of traffic".
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