The Ho Chi Minh City Center for Disease Control and Prevention said those arriving from September 5 would have to visit centers for tests while those not coming by air also need to make medical declarations at medical centers and designated facilities on arrival to get tested.
HCMC has gone over a month without local spread of infection, and on Monday allowed bars and dance clubs to reopen.
Da Nang eased social distancing measures on September 5, and the transport ministry allowed the resumption of public transport services to and from the city two days later. The central city, the epicenter of the second wave of Covid-19, has basically brought the outbreak under control with 10 days without new cases.
But many localities continue to screen arrivals from Da Nang. Hanoi requires them to make medical declarations and quarantine themselves at home for 14 days while Thua Thien-Hue Province next door to Da Nang requires them to furnish certificates showing they tested negative for the novel coronavirus.
Since July 25 Da Nang has recorded 389 Covid-19 cases.
Vietnam's Covid-19 tally is 1,054 with 35 deaths.