THE NUMBER OF NEW COVID-19 cases in Massachusetts is rising, raising concerns that the coronavirus could be picking up steam again.

The number of new confirmed cases averaged nearly 162 a day between July 1 and July 15, but the average rose to 203 from July 16 through Monday. That’s an increase of 25 percent.

Gov. Charlie Baker chalked the increase up to the emergence of case clusters around the state, including an outbreak at Baystate Medical Center in Springfield that was started by an employee who traveled out of state and was lax about wearing a mask after returning to Massachusetts.

“Positive test rates (positive tests as a percentage of all tests administered) have ticked up, going from about 1.7 to about 2 percent,” Baker said at a State House press conference on Monday. “Obviously, we would prefer to see zero new cases of COVID, but we know that’s just not going to be the case until we have a medical breakthrough like a vaccine.”

Baker on Friday announced tightened travel restrictions on people coming into the state starting August 1, but gave no indication on Monday that he would reverse course on the state’s phased reopening plan. He noted the state’s COVID-19 numbers are still well below where they were when the phased reopening began.

Combining confirmed and probable coronavirus cases, the state averaged  300 cases a day over the past week, an increase of 30 percent from the average two weeks earlier.

“This is a substantial increase and it is worth being concerned about,” said Robert Horsburgh, professor of epidemiology and biostatistics at Boston University.

When the Baker administration began to implement the Reopening Task Force’s first phase on May 18, the seven-day positive test rate was 9.6 percent. The numbers the Baker administration and Department of Public Health use are primarily based on a time frame of seven days. But public health experts like Horsburgh think that a two week assessment can provide more trend information.

“About the 14-day average- if you see something there, it’s more likely to be real because it is sustained. It’s the most conservative metric,” said Horsburgh.

A New York Times infographic map of average daily cases per 100,000 people shows that seven of Massachusetts’ 14 counties ended up with their data trending up over the last 14 days. Those are Berkshire, Hampshire, Middlesex, Worcester, Norfolk, Plymouth, and Barnstable counties.

Sen. Julian Cyr of Truro said the uptick in the numbers reflect what he is seeing on the ground. The cases started increasing on Cape Cod around July 17, two weeks after the 4th of July, which he said brought many visitors and high density events to the Cape.

“This is a clear positive trend,” said Cyr, who said he doesn’t see it as being a spike yet. Many of the cases, he said, were linked to a house party in Chatham, “which was just stupid,” and recent increased testing at skilled nursing facilities. “I think it’s clear we’re going to need to move back into a high state of vigilance at some point,” he said.

Baker said public health officials are analyzing coronavirus data for trends and are aware of “small clusters” associated with gatherings, including a private party in Chatham that resulted in at least 10 people testing positive for COVID-19. Another is connected to an employee at Baystate Health who Baker said traveled to a hot-spot state and was lax about wearing a mask, resulting in a number of employees and a couple of patients testing positive.

Baker is continuing to increase testing, targeting communities where the positive test rate is increasing but the amount of testing is declining. He earlier launched free testing starting July 10 through mid-August in Chelsea, Everett, Fall River, Lawrence, Lowell, Lynn, Marlborough, and New Bedford. Baker said 19,000 people have been tested so far in those communities.

“The first week the number of tests conducted increased by 48 percent,” Baker said. “We consider this a good thing.”

Of those 19,000, 17,000 have received results back with data showing the average positive test rate was 1.8 percent.

On Monday, Baker said he intended to expand the program to eight more communities — Agawam, Brockton, Methuen, Randolph, Revere, Springfield, Taunton, and Worcester. The positive test rate in those communities is currently 2.3 percent, nearly 50 percent higher than the statewide average.

Brockton, for example, has a 3.96 percent positive test rate over the last 14 days, with 71 new cases.

Experts are urging caution. Even before Baker held his press conference, David Rosman, president of the Massachusetts Medical Association, was trying to raise the alarm.

“Last four days in #Massachusetts had #COVID19 new positive tests over 200,” he tweeted. “Last time that happened?  Mid-June – on the way down.  The data is early, but it looks like we are on the way back up.  We should consider backing down a phase.  #wearamask. #SocialDistancing”