WATCH: White House will not reveal COVID cases among staff, will not address restrictions on the unvaccinated

She was asked if "the White House has had any additional staffers test positive for COVID-19?"

Psaki said that the White House policy is that "if there is an individual who is, has close proximity to any of the four principals as defined by the White House medical unit, along with CDC guidelines on what that looks like, we will then make that information available and immediately public to all of you. So, that has not been the case since we announced that policy, no," she said.

White House staffers have been vaccinated against the virus, though there have been instances of breakthrough cases. Most notably, a Biden aide tested positive for a case of COVID after interacting with Texas state lawmakers, Democrats, who had ventured to Washington, DC, as a means of fleeing from a vote in which they did not wish to take part in the state legislature. They have been trying in vain to meet with the President, though the White House has expressed support for their efforts to evade their legislative responsibilities.

The vaccination rate was at issue for White House reporters, one of whom asked "Does the President favor restrictions for unvaccinated people when it comes to restaurants, museums, concerts?"

Psaki had previously talked about the lagging vaccination rate in the US, and a increasing the vaccination rate among Americans has been a huge push from the Biden administration.

"The President favors using the CDC as his North Star," Psaki replied, "and what the health and medical experts are going to advise on how to save more lives and protect people."

"So, no, he doesn't think that there should be restrictions on unvaccinated people like some other countries have—" asked the reporter.

"He believes that we should be guided by the science and by the data, and so he will look to his health and medical team to advise on what steps he should take."