BEIJING—The coronavirus pandemic is making a hard situation worse for China’s growing number of job-seeking college graduates, intensifying pressure on Communist Party officials who see steady employment as critical to maintaining economic and social order.

The nearly nine million students expected to get their diplomas this year—China’s biggest graduating class in roughly a decade—will enter one of the toughest job markets in recent history. Even before the pandemic, the slowing economy was already throwing up fewer jobs for the swelling ranks of white-collar workers.

Jin Shu, a 22-year-old student in Beijing, accepted a teaching-assistant job at a local tutoring school in January, only to have it put on ice last month after the academy shut down. The pandemic, Ms. Jin said, “is like a cloud of smog and we have no idea what the road ahead looks like.”

The impact of the coronavirus, and the vast lockdowns and production suspensions that have been put in place to contain it, drove the country’s urban unemployment rate to a record high of 6.2% in February—above the official 5% rate that has held roughly constant over the years, despite the economy’s ups and downs.

Iris Pang, chief economist at ING Bank NV in Hong Kong, said the unemployment rate could rise to as high as 10% by the end of the year but local governments are likely to step in with stimulus to keep it from getting worse than that.