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Nagal recently lost his first round singles contest to Tallon Griekspoor at the US Open.
The indoor hard-court contest in Stockholm will be played on September 14-15.
“I was really looking forward to representing in the upcoming Davis Cup tie against Sweden,” Nagal wrote on social media.
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“I’m deeply disappointed to be missing this tie, but I have to listen to my body to prevent the back from worsening, so that I can finish the season strong and healthy. Good luck to the Indian team – I’ll be cheering for you all from home!” he added.
Nagal reached a career-high ranking of 68 in July but has dropped to 82 in the latest rankings. India’s highest-ranked singles player not being part of the Davis Cup tie is a big blow to the team.
Former national champion Ashutosh Singh has been named as new coach of the national team.