(Corrects to show the two cases found in Beijing are not both local cases, clarifies Changchun case details, paragraphs 13,22)

SHANGHAI/BEIJING, July 18 (Reuters) - Several large Chinese cities including Shanghai are rolling out new mass testing or extending lockdowns on millions of residents to counter new clusters of COVID-19 infections, with some measures being criticised on the internet.

China has reported an average of around 390 local daily infections in the seven days ending on Sunday, higher than about 340 seven days earlier, according to Reuters calculations based on official data as of Monday.

While that is tiny compared with a resurgence in other parts of Asia, China is adamant about implementing its dynamic zero COVID policy of eliminating outbreaks as soon as they emerge. Previously when a flare-up became a major outbreak, local officials had been compelled to take tougher measures such as month-long lockdowns, even at the cost of economic growth.

Persistent outbreaks and more closures could add pressure on the world's second-largest economy, which contracted sharply in the second quarter from the first after widespread COVID lockdowns jolted industrial production and consumer spending.

The commercial hub of Shanghai, yet to fully recover from the harsh two-month lockdown in spring and still reporting daily sporadic cases, plans to hold mass testing in many of its 16 districts and in some smaller areas where new infections had been reported recently, after similar testing last week.

"There is still an epidemic risk at the community level so far," the city government said in a statement.

Shanghai reported more than a dozen new cases but none was found outside quarantined areas, local government data showed on Monday.

"I'm speechless," said a Shanghai resident surnamed Wang, already subject to testing every weekend at her residential compound. "It sounds like a waste of resources that doesn't address the real problem."

The northern city of Tianjin, which launched multiple rounds of mass testing in recent months to curb earlier outbreaks, said on Monday it is again testing its more than 12 million residents, after two local infections were found.

In the northwestern city of Lanzhou, a lockdown in four major districts with around 3 million residents that started last week has been extended to July 24.

In the central Chinese city of Zhumadian, lockdowns for several million people in a few towns under its jurisdiction have been extended for a few days until Monday or Tuesday.