Hong Kong's rebound in Covid cases is not sounding alarm bells yet, but nevertheless some testing requirements are being updated, Chief Executive Carrie Lam said on Friday.

Lam said although the number of daily cases has now risen to over 1,000 again, pressure on public hospitals has not increased and the number of people in a serious or critical condition remains stable.

She said the government will, however, require care home workers to undergo a PCR test every two weeks, on top of their daily rapid tests, from June 22. They will also be required to get a third Covid jab in order to work, once the arrangements have been finalised.

All school children must also continue to undergo daily rapid tests until the end of the current academic year in August, the chief executive added.

Lam said the current circumstances do not require any tightening of social distancing measures.

"For the time being, I have to stress that this sort of upward cases, according to the experts, is not unexpected. Because we have almost returned to normalcy as far as social activities are concerned, so in a way this is not an alarm bell yet," Lam told a press conference.

"We will closely monitor the situation," she continued.

The CE also appealed to people to limit cross-family gatherings on Father's Day, adding that she has cancelled all her farewell meals, including those with legislators and senior officials.