TOKYO, July 5 (Reuters) - Japanese shares slipped on Monday, failing to gain a boost from a Wall Street rally after strong U.S. jobs data, as rising COVID-19 infections in Japan and elsewhere hurt cyclical shares. A disappointing showing by Japanese Prime Minister Yoshihide Suga’s Liberal Democratic Party (LDP) in a local election on Sunday added to the cautious mood. “The LDP’s recovery wasn’t strong, leaving concerns about the upcoming general election,” said Nobuhiko Kuramochi, senior strategist at Mizuho Securities. Nikkei share average lost 0.60% to 28,611.03, while the broader Topix dropped 0.40% to 1,948.41. That was a clear under-performance following new record highs scaled by Wall Street shares on Friday after jobs data for June showed robust hiring but limited signs of wage inflation. Many cyclical shares slumped, led by steelmakers, one of the most sensitive sector to the global economy on rising concerns about Delta variant of COVID-19. JFE Holdings lost 4.3%, while Nippon Steel shed 3.2%. Coronavirus cases in Tokyo have been on the rise over the past fortnight, hitting a five-week high and raising worries the government may declare its third state of emergency this year. Elsewhere, Softbank Group fell 5.2% to seven-month lows after China’s cyberspace regulator ordered smartphone app stores to stop offering Didi Global Inc’s app after finding that it had illegally collected users’ personal data. Softbank is a major backer of the Chinese ride-hailing start-up. On the other hand, some construction firms with strength in civil engineering gained after landslides triggered by torrential rains hit the central city of Atami at weekend, sweeping away 130 buildings. Raito Kogyo, a constructor with expertise in slope and foundation improvement, rose 1.5% CE Management Integrated Laboratory, which offers geological survey and disaster prevention systems, gained 3.7%. (Reporting by Hideyuki Sano; Editing by Shailesh Kuber)