Altogether 61 people have been confirmed as infected and 14 have died in the two weeks since Chinese authorities said they found the strain in humans for the first time.
"The public should somewhat restrain their anxieties to avoid this becoming a disaster for the whole poultry industry," the Global Times said in an editorial, adding that not eating poultry was "unfair to farmers".
It called the avoidance of such foods "excessive anxiety" and urged people instead to "demonstrate a collective spirit beyond individualism".
According to the World Health Organization (WHO), influenza viruses are inactivated by temperatures above 70C (158F) and it is therefore safe to eat well-cooked meat products.
The number of cases jumped from 40 over the weekend and spread for the first time beyond Shanghai and three nearby provinces, with two cases reported just west in Henan and one in Beijing, hundreds of kilometres (miles) away.
On Monday a boy in the capital, who had been put under observation because he was a close contact of an H7N9 patient, tested positive for the virus but was suffering no symptoms of illness, Beijing health officials said.
Experts fear the prospect of such viruses mutating into a form easily transmissible between humans, which would have the potential to trigger a pandemic -- but the WHO has said there is no evidence yet of such a development.
Health authorities in China say they do not know exactly how the virus is spreading, but it is believed to be crossing from birds to humans, prompting mass culls in several cities.
The United Nations' Food and Agriculture Organization has said H7N9 shows "affinity" to humans while causing "very mild or no disease" in infected poultry, making it more difficult to find the source of transmission.
That the virus could jump to humans, and cause mild or no illness in some people as with the boy in Beijing, meant it might spread more easily, said Jeremy Farrar, a Vietnam-based professor of medicine who has been studying H7N9.
A problematic virus "jumps across the species barrier, infects humans relatively easily, causes a spectrum of disease from mild to severe such that human-to-human transmission is made more likely -- that's what we have in H7N9", he said.
More lethal viruses might be less dangerous for the population as a whole because by killing off their carriers they could not spread as easily, he added, acknowledging that was a "slightly horrible view".
In 2003 Chinese authorities were accused of trying to cover up the outbreak of Severe Acute Respiratory Syndrome, which went on to kill about 800 people worldwide.
But China has been praised for transparency over H7N9, with the WHO and other international scientists saying it was pleased with the level of information sharing.
Farrar, who is with the Oxford Research Unit at the Hospital for Tropical Diseases in Vietnam, said the virus had been shared with labs around the world for study.