HONG KONG — Hong Kong’s government said Monday that it would close more border checkpoints, as some medical workers went on strike to demand a complete ban on entries from mainland China to limit the outbreak of the new coronavirus.

Carrie Lam, Hong Kong’s top official, has faced increasing calls from hospital employees, the business community and even some pro-government lawmakers to further tighten border controls with mainland China, where the virus emerged in December.

More than 2,500 medical workers in Hong Kong — mostly those considered to be nonemergency personnel — went on strike Monday morning to pressure the authorities to bar entries from mainland China. The number of strikers was expected to grow if the government did not relent.

The medical workers, who are members of a newly formed union, said they were worried that hospitals would be overwhelmed by a surge of coronavirus cases, as mainland Chinese seek to use Hong Kong’s health care system.