Hong Kong (CNN) Chinese Premier Li Keqiang has warned local officials not to hide new coronavirus cases, after the country reported several days of no locally transmitted infections in a major turnaround in its fight against the deadly pandemic .

Li, the country's second-in-command, urged local governments Monday to "seek truth from facts" and be "open and transparent" in releasing information on the epidemic.

"Being open and transparent means a new case must be reported once it's discovered. It is what it is. There must be no concealing or underreporting," he told senior officials tasked with battling Covid-19 during a meeting he chaired, according to an official government statement posted online Tuesday.

The Chinese premier was appointed the head of a central government task force -- or a "central leading group" as it is called -- to fight the coronavirus in January. He visited the city of Wuhan , the epicenter of the outbreak, back in late January, more than a month earlier than the tour by China's top leader Xi Jinping in March.

China's Premier Li Keqiang visited a construction site of a new hospital being built to treat coronavirus patients in Wuhan on January 27.

Li's warning appears to be part of a concerted effort to rebuild public trust amid persistent accusations that local officials deliberately downplayed the reality of the situation during the early stages of the outbreak.

It also comes as China faces increased scrutiny from overseas over its initial efforts to prevent the virus from spreading beyond its borders after it was first identified in Wuhan in December.

Since then, the virus has claimed 3,281 lives and sickened more than 81,000 people in China. It has put hundreds of millions under varying forms of lockdown and brought the economy to a halt.

Three months on, however, China appears to have turned a corner in its fight to contain the outbreak. Last Thursday, the country reported no local transmissions, and the number has stayed close to zero since. On Wednesday, China eased travel restrictions in Hubei, and the lockdown on Wuhan will soon be lifted too, on April 8.

At Monday's meeting, Li said that while the public had long looked forward to the good news of zero local infections, the statistics on the epidemic must be "truthful and accurate," urging local governments not to "hide or underreport cases in pursuit of zero cases."

Being transparent also means the public is less likely to let down its guard, which can help the implementation of epidemic control measures and prevent a rebound in cases, Li added.

On Tuesday, after new cases dropped to zero for five consecutive days, Wuhan reported a new confirmed case -- a doctor working at the Hubei General Hospital. The Wuhan Municipal Health Commission said in a statement that the possibility of cross-infection within that hospital could not be ruled out.

Staff members spray disinfectant at the Wuhan Railway Station on March 24.

Lingering threat

The threat of a so-called second wave continues to loom large in China.

To date, the virus has now spread to 170 countries and regions , according to figures compiled by Johns Hopkins University, and put nearly a third of the world's population -- or 2.5 billion people -- under coronavirus-related movement restrictions.

With the number of global infections surging past 423,000, a growing number of cases have been imported back to China from overseas -- many of them Chinese students and workers eager to return home as outbreaks flare up globally.

As of Tuesday, 474 imported cases have been reported by Chinese authorities, and cities like Beijing and Shanghai have imposed strict quarantine rules for international arrivals.

Workers wearing protective clothing check the temperatures of passengers entering the departures area at the Beijing Capital Airport on March 5.

But as the number of local transmissions in China decreases, concerns have grown around the reliability of the current data -- with many online questioning the role of asymptomatic carriers.

In China, only patients showing symptoms and positive results in nucleic tests are included in the official tally of confirmed cases. Asymptomatic patients who have tested positive are monitored and placed under quarantine until they develop symptoms or turn negative in later tests.

The World Health Organization, however, says in its guideline that "a person with laboratory confirmation of COVID-19 infection, irrespective of clinical signs and symptoms" should be counted as a confirmed case.

The risk posed by asymptomatic cases has drawn significant attention in China in recent days. Addressing these concerns, Wu Zunyou, a spokesman for the Chinese Center for Disease Control and Prevention, said at a news conference Tuesday that the asymptomatic patients had all been found when monitoring those who had come into close contact with confirmed cases.

"Will they cause the spread (of the virus)? No they won't," Wu said.

"Why? Because in China, under our current measures, all close contact (patients) have been placed under quarantine and isolated medical observation, and will be sent to hospital for diagnosis and treatment once they develop symptoms. So they won't cause any spread in society," he added.