Nicola Sturgeon issued the warning today as Scotland recorded its highest daily number of Covid-19 cases in two weeks.
Glasgow is among eleven council areas in Scotland which moved down a tier to level 3 of the Scottish Government's Covd-19 restrictions, allowing non-essential retail to reopen this morning.
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Hide AdBut Ms Sturgeon warned against a rush back to the shops.
She said: "I cannot emphasise enough to you today that the very, very last thing we want to see is overcrowding in or around shops and shopping centres."
The First Minister urged people to wait "a day or two" before shopping or to order online at today’s daily Coronavirus briefing.
She asked people to shop in their own area and not travel to or from Level 3 and Level 4 areas.
"For example, you should not travel to Edinburgh or Glasgow from outside these local authority areas, even for Christmas shopping," she said.
Chief Constable Iain Livingstone also warned that police will be ready to crack down on any breaches of the rules.
"Apart from legitimate exemptions we should not be travelling in and out of level 3 areas,” he added.
"I’ve consistently said I do not consider it appropriate or proportionate for police officers to set up roads blocks and routinely stop vehicles simply to enforce travel restrictions.
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Hide Ad"However where breaches do come to our attention officers will continue to respond with good sense, exercise discretion and take enforcement action where required.”
The First Minister said 31 Coronavirus deaths and 1,001 positive tests have been recorded in the last 24 hours.
It brings the total number of deaths under this measure to 4,070 and is the highest number of daily cases since November 26.
While Ms Sturgeon stressed the daily positivity rate is 4.6%, she told the Scottish Government's coronavirus briefing on Friday that the high number of cases - on the day retail reopened across much of the country - is a reminder the virus has not gone away.On Friday morning, 11 Scottish council areas - including
The First Minister also told the briefing that the Scottish Government's self-isolation payment will not be reduced by new self-isolation rules.
The four chief medical officers of the UK announced on Friday that close contacts of a positive case and those returning from countries without a travel corridor will be able to self-isolate for 10 days instead of the current 14 days from Monday.
A £500 support payment has been given to those on low incomes who are asked to self-isolate.
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Hide AdMs Sturgeon said: "It's important for me to be clear they will have no impact - these changes - on the payment that is available for people on low incomes who require to self-isolate.
"That payment will be maintained at £500."
The First Minister also said she is "pleased" with the uptake of a community testing programme in Johnstone, Renfrewshire.
She said more than 5,000 people came forward to be tested - about 40% of the target population.
"That is a good uptake and one that we are pleased about," Ms Sturgeon said.