Boston Mayor Marty Walsh repeated Friday that there remain “no plans for a lockdown or shelter-in-place,” in the City of Boston or statewide, but he warned that it could still be coming.

Walsh told Boston Public Radio hosts Jim Braude and Margery Eagen that he remains in close communication with Gov. Charlie Baker, who has the authority to issue some form of “shelter in place” order under statewide emergency powers, and that he is aware of no such plan.

Walsh has repeated that message on a daily basis this week, including in a televised address to Boston residents Tuesday night.

Walsh’s statements were affirmed later Friday by Massachusetts Gov. Charlie Baker, who told reporters that he wanted to “dispel, once again, recent rumors about a shelter-in-place order.”

“Massachusetts is not planning any forced shelter-in-place order,” Baker said. “We have shut down enormous parts of our economy in our communities across the commonwealth. We are very much in social distancing and shutdown mode here in Massachusetts based on what we’ve already done.”

But Walsh has also been careful to tell the press and the public that he cannot rule out the possibility of some kind of shelter in place or “lockdown” order, whether from his office or statewide, or via an order at the federal level.

Walsh noted that California ordered residents to stay home except for essential needs; Italy has banned all public events; Hoboken N.J. has ordered self-isolation.

“We are heading potentially to that… We have to wait and see what happens,” Walsh said.

He said government officials are “monitoring the numbers to see what the curve looks like.” But meanwhile people should just distance themselves from each other without waiting for a government order.

Walsh has said he strongly favors voluntary measures to reduce the spread of coronavirus and that in any potential order that could yet come down he foresees, parts of life would not be shut down, like providing and selling food..

"People need food," Walsh said.

Walsh’s statements were affirmed later Friday by Massachusetts Gov. Charlie Baker, who told reporters that he wanted to “dispel, once again, recent rumors about a shelter-in-place order.”

“Massachusetts is not planning any forced shelter-in-place order,” Baker said. “We have shut down enormous parts of our economy in our communities across the commonwealth. We are very much in social distancing and shutdown mode here in Massachusetts based on what we’ve already done.”

In a press conference Friday afternoon, Walsh urged the public to continue practicing social distancing, and chided certain behaviors he said are not helping.

Residents should resist the urge to have friends, family and neighbors over, the mayor said. And he warned that landlords and real estate agents should not be showing occupied apartments to prospective renters.

Walsh also said that with plummeting commuter traffic, there has been more speeding in certain parts of the city — and that, he said, has to stop.

“We’ve come a long way on road safety in our city, we’re focused on saving lives right now, so I’m asking people, please obey the speed limit,” Walsh said. “I don’t want to have to set up speed traps for people who should understand and obey the law. That’s something we don’t need right now in the City of Boston.”