Murray and the fiery Italian had a few heated exchanges on the court, but their tempestuous second-round clash continued afterwards, it is claimed in a report in The Times.
The three-time Grand Slam champion, who lost the match 7-6 2-6 7-6, was enraged by the world number 12 shouting out as he attempted a volley at the net, leading to him telling the Italian to "shut up".
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The Times reports that the pair did not let things go after shaking hands at the conclusion of the match.
"[Murray and Fognini] were involved in another heated verbal exchange behind the scenes at the Qizhong Forest Tennis Centre," the report read.
"A small number of players, coaches and officials watched awkwardly as they aired their grievances with each other in a communal area."
Fognini's act of hindrance in yelling out during a crucial point in the match angered Murray, who ranted at the umpire and later pushed his opponent's hand away following their brief handshake.
On the court, Murray had said to Fognini after he shouted out during the point: "You say the same to everyone.
"Mate, you do the same in every match. It doesn’t matter who you’re playing."
The 32-year-old Brit informed the umpire of his frustration at Fognini in the same exchange.
"So what happened… When I had a volley on top of the net, he shouts…
"I had a volley on top of the net. He shouts, and then tells me ‘don’t look at me’.
"I’m like ‘you just shouted in the middle of the point’."
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