It a slight increase from 62 percent registered in the week of May 27.
CNN’s Harry Enten said Mr Biden is “in danger” of missing his vaccination target.
He wrote in the publication that the problem was “that we really haven’t seen the vaccination rate pick up since they become readily available in April. We’ve only seen declines pause.”
The analyst added: “The fact is, we’re running out of people who have indicated that they want the vaccine as soon as possible.
“The latest Kaiser Family Foundation poll from late May found that 66 percent of Americans either had received a first Covid-19 vaccine dose or wanted one as soon as possible.
“This 66 percent is near the same percentage as where the current vaccination rate trendline indicates we’ll end up by July 4.”
Mr Enten concluded that to achieve the President’s 70 percent target, “some people will have to be convinced” to receive the jab in the next month.
He added: “The key over the next month will be for these unvaccinated people to have a sense of urgency to receive their first dose.”