As Massachusetts entered phase one of Governor Charlie Baker’s plan to reopen the economy, the director of the Harvard Global Health Institute urged state leaders to ramp up testing “a lot” before moving on to phase two.

“We’re still pretty far behind where I’d like for us to be,” said Dr. Ashish Jha. “While we do have many more tests per capita than most places, the problem is we also had a bigger outbreak than almost any other place. And given the size of the outbreak, we need a lot more tests.”

Jha told Jim Braude on WGBH News’ Greater Boston Monday that he feels comfortable with the activities permitted so far in phase one, including manufacturing and construction. But he said the state’s current level of testing is not enough to safely move into phase two, which will permit broader restaurant, hotel and retail operations.

“Before people really start heading outside and going to restaurants and interacting with each other much more aggressively, I’d like to see a lot more testing in place,” he said. “If our testing flattens out where we are right now, we’re going to end up getting into trouble in upcoming weeks.”

Nationally, there has been some progress in testing. On Sunday, the country conducted more than 422,000 tests in total — single-day high. But that’s still less than half of the minimum 900,000 tests per day Jha has recommended.

“We’re still not where we need to be by any stretch of the imagination, but we are better,” he said. “You gotta keep getting aggressive on testing and ramp up further.”

In the long run, though, Jha has confidence the country will be able to meet those goals.

“I’m very optimistic that we will get to the number of tests we need and actually surpass those numbers. Not in the short run. The short run really requires aggressive federal leadership and I have come to conclude that we’re not likely to see that anytime in the next few weeks,” he said. “What makes me optimistic is there are all sorts of new types of tests coming online … and those will let us get to millions of tests a day, even without White House leadership on this.”

Jha also weighed in on an early breakthrough from a Cambridge biotechnology company working towards a coronavirus vaccine.

Moderna reported Monday that the eight people who participated in their first round of testing developed coronavirus anti-bodies. Jha said the news called for happiness “tempered with realism.”

“There have been long histories of things that look pretty good in phase one, phase two, even going into phase three – but don’t end up panning out. So, I’m not betting on this one, per se,” he said. “What this did for me was made me more confident that eventually we will get a vaccine and that makes me feel better.”

Jha said he’s still not holding out hope for the president’s prediction of vaccine ready for widespread use by the end of the year.

“It’s very hard for me to see how we are going to have large numbers of safe, effective vaccines by December,” he said. “I’m probably thinking mid-2021 … if everything goes well.”