Donald Trump Jr, the son of US President Donald Trump, tested positive for Covid-19 this week, although he is experiencing no symptoms, according to his spokesman.

Mr Trump Jr tested positive at the start of the week and has been "quarantining at his cabin since the result", the spokesman said.

"He's been completely asymptomatic so far and is following all medically recommended Covid-19 guidelines," he said.

Earlier, Andrew Giuliani, the son of the president's personal lawyer Rudy Giuliani, also said he tested positive for Covid-19.

"This morning, I tested positive for COVID-19," Andrew Giuliani, who joined the Trump White House's Office of Public Liaison and Intergovernmental Affairs in 2017, said on Twitter.

"I am experiencing mild symptoms, and am following all appropriate protocols, including being in quarantine and conducting contact tracing," he added.

Mr Giuliani attended his father's press conference Thursday at the Republican National Committee headquarters in Washington, according to multiple reports.

The elder Giuliani and other Trump campaign lawyers spoke without masks from an indoor podium, to an audience of dozens.

Several White House staffers have tested positive for the disease in recent weeks, including chief of staff Mark Meadows, while six members of Congress have tested positive this week.