Azhar has been widely criticised for his unimaginative captaincy since taking over from Misbah-ul-Haq, who retired from the 50-over format following the World Cup last year.
He has led his country to 15 losses in 25 matches, with nine wins and one no result. The team have dropped to ninth in the one-day rankings.
Sarfraz Ahmed, who had been tipped to replace Azhar as one-day skipper, will lead the side in the three-match Twenty20 series starting in Dubai from Friday.
Media had reported that the Pakistan Cricket Board wanted Azhar to step down but he resisted the move.
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PCB chief operating officer Subhan Ahmed said a decision on whether to give former Twenty20 captain Shahid Afridi and off-spinner Saeed Ajmal a farewell match would be taken at a meeting on September 26.
There were reports the PCB's selection committee headed by former captain Inzamam-ul-Haq wanted to give Afridi a swansong match, but the move was opposed by other officials.
Ajmal has lost his place in the team after failing to deliver wickets with a remodelled action following a chucking suspension in 2014.
Ahmed also said the PCB had not ruled out picking ex-captain Salman Butt, one of three players punished for spot-fixing in 2010.
Butt, Mohammad Asif and Mohammad Amir had their bans lifted in September last year. But so far only Amir, who was 18 at the time of his ban and garnered widespread sympathy, has staged an international comeback.
"There is no bar on Butt's selection," said Ahmed. "Our selection committee can select any player.
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