The Welsh Government may have to consider stricter enforcement if people continue to break Covid-19 rules, according a minister.
Eluned Morgan said they would need to "look at the evidence as to who is breaking the rules".
She also said Welsh ministers had not had a chance to discuss a change of policy on fines in England.
The UK government is introducing £10,000 fines for people who fail to self-isolate.
Its new measures also include a one-off £500 support payment for those on lower incomes.
International Relations Minister Ms Morgan told BBC Politics Wales: "We need people to follow the rules and we need to make sure there is carrot as well as stick.
"We want to know a bit more about the carrot.
"They're saying that people will have £500 to help them to stay home.
"If that's the case, we want to know whether that money will be coming to Wales as well," she added.
The Welsh Government said they already had the powers to potentially introduce a system to fine people up to £1,000 if they do not self-isolate.
"Whether or not this is made a legal obligation, it is crucial that anyone with symptoms of coronavirus stays at home to prevent the onward spread of this infectious disease - this includes while waiting for the results of a test," they said in a statement.
Merthyr Tydfil council leader Kevin O'Neill claimed on Saturday that some people in the area had "lost their discipline".
Rates in Merthyr Tydfil over the past week have overtaken neighbouring Rhondda Cynon Taf, which was placed in a local lockdown on Thursday.
Wales' deputy chief medical officer Dr Chris Jones said there was evidence "people have become a little less concerned about the risk that the virus poses and are taking more risks in their everyday lives".
"The crucial thing is that when somebody has symptoms, they isolate themselves from contact with others," he told BBC Radio Wales' Sunday Supplement programme.
"And that's quite a tough thing to do."
He also said there was a lot of variation in the rate of transmission of the virus across Wales, with hotspots in the south.
In light of the differing picture across the country, he said taking Wales-wide "measures may be disproportionate for people in areas where the virus is less troublesome".
Most of Wales' Covid-19 tests are processed at UK-wide lighthouse labs, which are struggling to deal with a backlog of tests.
The Welsh Government has pledged more tests would be available next week that will be processed by the Welsh NHS.
Asked when the Welsh Government became aware of testing problems at Lighthouse labs, Ms Morgan said: "We clearly became aware when people were unable to get their tests.
"There's been considerable pressure from the Welsh Government constantly asking the health minister in England what they're doing, how they can improve the situation and we've had to pick up the slack."
Pressed on whether the Welsh Government had been too slow to shift the processing of the tests from the lighthouse labs to Welsh NHS labs, the minister said: "We have been nimble and we have tried to change things.
"We've moved to 24-hour processing at the three labs in Wales; one in Swansea, one in Cardiff and one in Rhyl.
"We've tried to shift the mobile analysis that's happening from the Lighthouse Labs to Public Health Wales and we're making sure that we're increasing the number of mobile units as well," she added.