Devon County Council has sent an all-party message to holidaymakers and second home owners: Stay away from the South West during the current crisis.
And the council is calling for much tougher penalties to be imposed on people who flout the rules.
Council leader John Hart said he was planning to meet the leaders and chief executives of all Devon's district councils to discuss co-ordinated enforcement action against holiday providers who continue to take bookings.
"As we head to Easter, we want to send a very clear message to holidaymakers and second home owners," said Mr Hart.
"Devon and the South West are closed. We will welcome you with open arms when this is all over but right now please stay away.
"We currently have low coronavirus infection rates in the South West but, if you come here, you stand a chance of bringing it with you and we do not want it under any circumstances.
"We want the message to go out loud and clear and we want our MPs to stop those organisations which are still advertising holidays here."
Labour leader Rob Hannaford said: "It's highly damaging and irresponsible for people to be coming to the South West to holiday accommodation or second homes and we want more police spot checks on our borders.
"We have a lot of elderly people here who are most susceptible. We are at the bottom of the regional tables for coronavirus infection and we want it to stay that way."
Liberal Democrat leader Alan Connett said: "We want people to come here when this is all over but for now the message is clear: stay home and stay safe."
Independent group leader Frank Biederman said: "We need the Government to introduce huge fines for people who flout the regulations and we really need to emphasise that we are closed. The NHS can't care for visitors as well as our own residents.
"The vast majority of our tourism businesses are closed and are taking a big financial hit for the benefit of the community but we need to crack down on those who refuse to do so."