The rate of transmission - which is the rate at which COVID-19 spreads from person to person - exceeded 1.0 for the first time in 10 weeks, Murphy said.
That means, on average, each new COVID-19 case leads to one more new case.
As rates of COVID-19 hospitalization, ICU patients and ventilator needs go down, @GovMurphy is concerned with the rising rate of transmission. It stands at 1.03 meaning for every positive COVID-19 case, it leads to (on average) one additional case.— Maggie Kent (@MaggieKent6abc) July 6, 2020
Meanwhile, Murphy said there are several outbreaks across the state that have been directly tied to COVID-19 hotspots across the country.
That includes 12 out of 13 new cases in Hoboken, along with several new cases elsewhere in north Jersey that were tied to a wedding in Myrtle Beach.
There is a 14-day quarantine for those who travel from those hotspots. A list of those states can be seen at covid19.nj.gov/travel
Murphy again urged state residents to wear face masks to help prevent the spread of the virus.
"I do not want to have to hit another pause on our restart because a small number of New Jerseyans are being irresponsible," Murphy said.
There were some positive developments on Monday: the number of hospitalized patients, patients in critical or intensive care, and the number of ventilators in use all went down.
Starting Monday, youth day camps, in-person summer education, and graduation ceremonies were allowed in the state.
NJ Transit rail and light rail returned to a full weekday schedule.
Murphy had earlier announced the reopening as part of Stage 2, of three. Before the Fourth of July holiday, nearly a dozen different sectors reopened, though with limited capacity. They include: amusement parks, aquariums, boardwalk arcades, bowling alleys, casinos, libraries and museums.
Rail riders and NJ Transit workers must wear masks under the governor's reopening mandate.
New Jersey's coronavirus trends have continued to head in the right direction, while other states are seeing cases spike again.
Twenty more deaths were announced, increasing the statewide total to more than 13,300. More than 200 positive cases were reported, bringing the total amount of cases to about 173,600.
Murphy, who has been holding daily virus press conferences Monday through Friday since mid-March said that starting this week, they will only be held on Mondays, Wednesdays and Fridays.
For most people, the virus causes mild or moderate symptoms. Older adults and people with existing health problems are at higher risk of more severe illness or death.
The Associated Press contributed to this report