Mayor Walsh used his press conference on Tuesday to warn Bostonians against letting their guards down in the struggle to contain the COVID-19 virus amid a slight rise in reported cases in Massachusetts and more stringent restrictions for people who travel here from outside of the region.

“If we think we’re winding down with COVID-19, we’re not,” the mayor told reporters outside City Hall. “If we think of it like a sporting event, we’re probably at half-time which means we’ve got another 6, 7, 8, or 9 months to go. So, we still have to be very careful.” 

As of Tuesday, coronavirus cases in the city have reached a total of 14,022, with 10,090 recoveries and 727 deaths. Walsh said that 51 new cases — and a single death— were reported in Boston on Monday, a cumulative number that included Saturday and Sunday.

State public health officials reported 182 new cases on Monday and announced the recent deaths of 7 people with the disease, raising the state’s cumulative caseload to 108,562 and increasing the death toll to about 8,320. When also counting people who have probably died from the virus, the death count is close to 8,540 since March 20. 

Monday’s report from the Department of Public Health also showed that the number of people hospitalized with COVID dropped by 14 to 350 as of midday Monday. In late April, there were more than 10 times that number hospitalized in Massachusetts with the respiratory disease.

Still, there were nearly 500 new cases confirmed in Massachusetts over the weekend and the percentage of tests that are coming back positive is rising. The number of daily new cases, which had settled at fewer than 200 a day earlier in the month, has been above 200 each of the last four days.

“I’m going to repeat what we’ve been repeating,” Walsh said. “People need to socially distance, avoid large crowds, in-person gatherings or parties… Also we’re asking that people avoid being outside during the heat wave.” 

The mayor urged Bostonians to refrain from hosting in-person birthday parties or cookouts. “Be very careful, you don’t want to see outbreaks of COVID in your yards or in city parks; that’s another reason why we are not going to be having parades in the city in the summer or the fall.”

 “It amazes me that there are some elected officials in the country that are still refusing to wear a face mask and talk about the importance of them,” Walsh said. “In Boston, when we reopen it doesn’t mean we are relaxing any of the precautions we have in place. We don’t want to start going backwards.” 

Citing four consecutive days of national COVID-19 death totals above 1,000, he also talked about his concerns about thousands of students who will be flocking to Boston area colleges next month from other parts of the country. He said he is in frequent contact with college and university officials about precautions they are taking, including safe housing options that involve the use of hotels.

Universities need to reach out to neighborhoods that may be affected by student housing changes, said the mayor, who plans to meet this week with college presidents to further discuss their reopening plans. He said he will discuss the importance of knowing immediately about any significant rise in coronavirus cases and how universities plan to adhere to state quarantine orders for students living on and off the campuses.

Last week, Boston Public Schools Superintendent Brenda Cassellius presented a “working’’ plan to the School Committee, detailing three separate setups for the upcoming syear, including a completely virtual format, in-person learning, and a hybrid model of both. 

“I want to stress that it’s a draft of the reopening plan,” Walsh said on Tuesday. “BPS is following public health guidelines for reopening schools. They’re been gathering feedback for months via survey, focus groups, and community meetings.

“Right now,” he said, “we are looking at a hybrid model that would assign students into groups and bring them into schools on a rotating basis. That’s what we’re looking at today, but no matter what model is chosen, BPS has fully developed a plan for all remote as well if the cases go up before Sept. 10 or after that.” 

“It’s important that if there’s a significant increase in cases, we have a chance to know it and get on top of it immediately,” added Walsh. 

“There’s no one size that fits all, but all I know is that on Sept. 10, it will be almost six months to the day that students have not been in the classroom,” he said. “As we get closer to school, based on the science and numbers we’ll determine which option we go forward with.” 

Walsh had a few words of encouragement for residents. “No matter how tough it’s getting, I’m asking everyone to remember that we are Bostonians and we are strong,” he said. 

“We will get through this. Just think about taking it one day at a time. This, too, shall pass and we will move forward and come out of this stronger than before.” 

In Somerville, Mayor Joe Curtatone has taken a slower approach to allow business and social activity to resume. While most of the rest of the state has advanced to Phase 3 of the administration’s plan to open movie theater, gyms and more, Somerville is waiting until at least early next month to permit most of those Phase 3 businesses.

In an interview Sunday with WBZ-TV’s Jon Keller, Curtatone defended his approach and said he has two goals: “to ensure the public health, safety and wellbeing of everyone in our community and also to make sure that in any reopening, that it sustainable.

“As we move forward and as we have been moving forward, we have to commend the governor, his administration, the commonwealth and everyone out there who has done their part to flatten the curve,” he said. “But there are lessons to be learned and there’s data that we should be fully looking at.”

State House News Service reports contributed to this article.