Tim Kaine says he and his wife tested positive for coronavirus antibodies

"We each tested positive for coronavirus antibodies this month. While those antibodies could make us less likely to be re-infected or infect others, there is still too much uncertainty over what protection antibodies may actually provide," Kaine said in the statement.

He continued: "So we will keep following CDC guidelines -- hand-washing, mask wearing, social distancing. We encourage others to do so as well. It shows those around you that you care about them."

Kaine, 62, explained that he had been treated for the flu earlier this year but experienced an onset of new symptoms in late March and that his wife, Anne, then "experienced a short bout of fever and chills, followed by congestion and eventually a cough."

"After Anne got sick, we each talked to our health providers in early April and they thought it possible that we had mild cases of coronavirus. We were both at home in Richmond, working remotely and isolated from others," he said, adding that a shortage of Covid-19 tests prevented them from being tested for the virus, but that they "continued isolating" and were symptom-free by mid-April.

CNN reported earlier this week that antibody tests used to determine if people have been infected in the past with Covid-19 might be wrong up to half the time, according to new guidance from the US Centers for Disease Control and Prevention.

Kaine, who was the Hillary Clinton's running mate on the 2016 Democratic presidential ticket, is not the only US senator known to have had the deadly virus. In late March, Republican Sen. Rand Paul of Kentucky tested positive for coronavirus, but has since recovered.

In addition to Kaine and Paul, at least four House members have announced they tested positive: Republican Reps. Mario Diaz-Balart of Florida and Mike Kelly of Pennsylvania, and Democratic Reps. Joe Cunningham of South Carolina and Ben McAdams of Utah. Democratic Rep. Nydia Velázquez of New York has said she had "been diagnosed with presumed coronavirus infection."

The virus has so far infected more than 1,700,000 Americans and claimed the lives of more than 100,500 Americans, according to a tally from Johns Hopkins University.