A highway sign urges out of state visitors to self-quarantine for 14 days if they plan on staying in Massachusetts due to the virus outbreak along Route 93 southbound in Wilmington, Mass., Monday, March 30, 2020. The new coronavirus causes mild or moderate symptoms for most people, but for some, especially older adults and people with existing health problems, it can cause more severe illness or death. Credit: Charles Krupa | AP

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AUGUSTA, Maine — Gov. Janet Mills said Tuesday that she will issue an order “insisting” that out-of-state visitors to Maine self-quarantine for two weeks in what would be one of her strongest mandates yet in fighting the new coronavirus outbreak.

That would build on a stay-at-home order announced by the Democratic governor on Tuesday that will bar Mainers from leaving their homes in most cases except for going to essential jobs and buying necessities including groceries. Only nine states have instituted mandatory quarantines for all travelers, according to the Kaiser Family Foundation.

[Our COVID-19 tracker contains the most recent information on Maine cases by county]

At a Tuesday news conference, Mills said she cannot close the state border or “pull up the Maine-New Hampshire bridges.” But she said she would issue an order in the coming days mandating quarantines for travelers while repeating past warnings that people from population centers should not see Maine as a place to avoid the virus.

“Our health facilities may soon be overcrowded and overwhelmed,” she said. “If you get sick or if you are sick, treatment may be scarce or even unavailable to you and the people of Maine.”

Under an emergency declaration issued in mid-March, Mills has sweeping powers to respond to the coronavirus, which has sickened 303 and killed five in Maine since the first case was reported less than three weeks ago, but she faces constitutional limitations at the border.

Shutting down the Maine-New Hampshire border, for instance, could be challenged under the 14th Amendment, which says states cannot “abridge the privileges or immunities of citizens of the United States,” said Joseph Reisert, a government professor at Colby College.

[Read our full coronavirus coverage here]

To justify infringing on an individual’s rights, Reisert said, a state generally must show that it has a compelling reason for a particular policy, and that the goal it was trying to achieve through that action could not be achieved in a less intrusive way. A quarantine for travelers is a likely example of a less intrusive way the state can aim to stop the spread of the virus.

Massachusetts and Vermont are the only New England states to mandate quarantines so far, while other states including Texas have asked travelers from certain hard-hit states to quarantine or applied mandates to certain people who have come to their states by air.

The federal government issued a guidance on Saturday advising people from New York, New Jersey and Connecticut, three states that account for roughly half of all cases in the country, to not travel out of state for nonessential purposes.

Mills noted the state has also encouraged snowbirds — older residents who live in warmer states for the winter — to stay where they are. The issue has touched a nerve for some. Police in Knox County said Friday that a group of men cut down a tree outside a residence in Vinalhaven in an apparent effort to prevent people from New Jersey from leaving the property.

State parks have noted higher numbers of visitors in recent days as cooped-up individuals look to escape to the outdoors, and the state has taken some measures to close many coastal beaches and parks that attract locals and travelers alike.

In a letter to the administration of President Donald Trump pressing for more protective equipment, the state’s congressional delegation noted that Maine’s “proximity to more densely populated areas with active hotspots also makes it a potential refuge destination and increases the risk of spread.”

[Interactive map: The number of confirmed coronavirus cases in each state]

Nirav Shah, the director of the Maine Center for Disease Control and Prevention, said on Monday said people without symptoms who travel to Maine may have a slightly higher risk of transmitting the virus than Mainers without symptoms, referring to the U.S. CDC guidance.

But Shah and Mills have both emphasized over the past two weeks that the coronavirus is spreading here regardless, citing community transmission in Cumberland and York counties, and people should neither alter their social distancing efforts based on where cases are nor think that they are safe from the virus in Maine.

Watch: What you need to know about handwashing during coronavirus