"We are tracking at this point a ship that may have shared crew with the Diamond Princess or the Grand Princess," said Mike Pence.
"There's a lot of unnecessary hysteria out here. And I would just urge everyone to chill a bit, use some common sense," he said.
Biton, 75, the husband of Rachel Biton, who contracted the virus while on the ship and had to spend a week in a military hospital in Japan, returned to Israel earlier this week.
The antiviral drug remdesivir, developed for Ebola, is being tested on a patient who was infected with coronavirus on the "Diamond Princess" cruise ship and brought to the US.
It is still unclear if any of the Israeli embassy officials have the coronavirus.
Rachel Biton is one of the four Israelis who contracted coronavirus while aboard the Diamond Princess cruise ship in Japan.
The woman in her 60s disembarked the "Diamond Princess" in Yokohama on Wednesday following a two-week quarantine on board, but was found to be positive following another test.
More than 620 passengers on board have been infected with the coronavirus, the most outside mainland China.
Sheba doctor: ‘On our end, it is not a big surprise’
Fourth Israeli tests positive, transferred to Japanese hospital