The First Minister of Wales has asked people to “think every time they make a journey” and avoid unnecessary travel.
Mark Drakeford said he was appealing to people to follow the travel advice, which he said would not be “policed in the conventional sense”.
Under new measures coming into force across Wales on Thursday, pubs, cafes, restaurants and casinos must operate as table service only and close at 10pm.
Off-licences including supermarkets will also be stopped from selling alcohol at the same time.
A £500 payment will be provided to support people on low incomes who are asked to self-isolate.
Asked about people avoiding non-essential journeys, Mr Drakeford told BBC Breakfast: “Well it’s advice to people, it won’t be policed in the conventional sense.
“We’re simply appealing to people to think very carefully about journeys they make.”
Mr Drakeford said the previous “stay local” message in Wales was “undoubtedly successful” in protecting the south west and north of Wales from the spread of Covid-19.
“The more people we meet, the more journeys we make, the more risks we run to ourselves and others,” he added.
“So it’s an appeal to people to think carefully about those journeys.
“If they’re necessary you must make them. If they’re not necessary, please don’t travel unless you have to. That is the message here in Wales.”
He later told BBC Radio 4’s Today programme: “What I’m asking people in Wales to do is think every time they make a journey.”
Asked if that meant no holidays, Mr Drakeford replied: “Well, it’s very possible to have a holiday in Wales without travelling very far at all.
“People are going to make those decisions in their own circumstances so we’re not saying no holidays to people.”
He said people in England should also think “very carefully” before making non-essential journeys into Wales.
But Mr Drakeford told the BBC it was a “difficult balancing act” between the needs of the economy and public health.
“Many people who come from England to Wales on holiday are an important part of our tourism economy, many people who come from England into Wales are coming to work in Wales as part of the economy,” he added.
He said Wales had taken a “more cautious” approach than England in lifting previous lockdown measures.
People in the country have always been encouraged to work from home where possible.
Only six people are able to meet indoors and must be part of a single extended household.
Face coverings must be worn on public transport, in shops and in enclosed public spaces across Wales.
Mr Drakeford said he had previously written to Boris Johnson about financially supporting those asked to self-isolate.
“There’s no doubt that some people on low incomes in Wales have found themselves feeling forced to do the wrong thing,” he told the Today programme. “Going into work when they know they’ve got symptoms because they simply wouldn’t be able to survive without the income that work brings them.
“I wrote to the Prime Minister nearly two months ago asking him to agree a scheme that would remove that perverse pressure on people to do the wrong thing. The £500 payment is an incentive to do the right thing.”
Mr Drakeford said many employers in Wales paid people in full for their two-week period of self-isolation and the payment would put those on low incomes on a “level playing field”.
Six areas of south Wales – Caerphilly county borough, Rhondda Cynon Taf, Bridgend, Merthyr Tydfil, Newport and Blaenau Gwent – are under stricter restrictions as part of local lockdowns.
People must not enter or leave the areas without a reasonable excuse, and they can only meet outdoors and must not meet members of their extended household indoors.
On Tuesday, Public Health Wales said a further 281 positive cases of Covid-19 were recorded – the highest daily figure since April 17.
Of the new positive cases, 77 were in Rhondda Cynon Taf, 34 were in Bridgend, 30 in Cardiff, 28 in Swansea and 20 in Merthyr Tydfil.
No further deaths were reported on Tuesday, with the total in Wales since the beginning of the pandemic remaining at 1,603.