* Shanghai karaoke venues suspend operations after fresh outbreak

* Shaanxi governor calls for 'war-time' state to stamp out cases

* China, HK stocks drop on COVID flare-ups (Adds Shanghai details, latest Beijing caseload)

By Brenda Goh and Roxanne Liu

SHANGHAI/BEIJING, July 6 (Reuters) - China is fighting nascent COVID-19 flare-ups across the country with mass testing and fresh restrictions, including in weary Shanghai where new cases have been linked to a building which houses a karaoke lounge that was operating illegally.

Pressure is mounting on officials to avert a wider spread and disruptions similar to the painful and costly isolation that Shanghai, China's most populous city, suffered in April and May. Those business disruptions rippled across the global economy.

"Several Chinese areas are facing local outbreaks and infections have emerged at the community level in Shanghai," city health official Zhao Dandan told reporters on Wednesday.

"There should be no slacking," Zhao said.

While the latest daily caseload of just over 300 infections is insignificant by global standards, the officials' reaction shows China's firm commitment to its policy to eradicate all outbreaks.

However, fears that further lockdowns to control the spread of the disease could curb activity in the world's second-largest economy weighed on Chinese stocks, and financial markets worldwide.

China is the only major economy digging in its heels on a "zero-COVID" policy aimed at promptly eradicating all outbreaks, while the rest of the world tries to co-exist with the virus.

Shanghai listed 26 addresses of buildings under lockdown on Wednesday, taking the total to 31. One COVID case was suspected in one of the iconic International Financial Centre twin towers, and office workers on two floors have been taken to quarantine as close contacts, according to staff in the building.

The commercial hub of 25 million people reported 24 new cases for Tuesday versus Monday's eight. It is testing all residents in nine of its 16 districts, and some from other areas, from Tuesday to Thursday.

Shanghai already requires residents to get tested frequently in order to enter shopping malls or take public transport. Authorities have suspended operations of karaoke lounges, but other recently-reopened cultural venues such as libraries will stay open. Cinemas are due to reopen on Friday.

'WAR-TIME'

Beijing, which reported three new cases on Wednesday as of 3 pm, urged transport hubs and hotels to check the body temperature of visitors and proof of negative COVID test results. From July 11, only vaccinated Beijing residents can enter crowded venues, officials said.