In March, Italy's antitrust authority fined the former phone monopoly 116 million euros (104 million pounds), saying it had conducted a "premeditated anti-competition strategy" aimed at hindering competitors' investments in ultra-fast broadband.
That prompted Italian broadband operator Open Fiber to ask TIM for 1.5 billion euros in damages, sources have said. .
TIM, which appealed against the antitrust ruling, asked an Italian administrative court to freeze the payment pending a decision on the merit of the case. But the court ruled there were no compelling reasons to satisfy the request, the document showed.
The Italian competition watchdog had already extended the deadline for payment of the fine until Oct.1 due to the coronavirus emergency.
TIM declined to comment on Tuesday's ruling.
The company's shares were down 2.8% at 1430 GMT, against a 0.5% rise in Italy's all share index.
(Reporting by Domenico Lusi, Elvira Pollina; editing by James Mackenzie and Mark Potter)