The first minister has acknowledged extending the lockdown is damaging people’s sense of mental well-being.
Mark Drakeford said “we should all be anxious” about how long it can be sustained.
He said he hopes changes to the regulations will help people “do the bigger things we’re asking of them”.
From Monday, people in Wales will be allowed to go out to exercise locally more than once a day and garden centres can reopen.
Mr Drakeford said only the “very smallest and most modest steps” could be taken because a small increase in the reproduction rate of the virus would lead to a significant increase in deaths.
Speaking on BBC Radio 4’s Today programme, Mr Drakeford said: “The evidence that we heard from behavioural scientists in making our decisions was that if you can offer people a little bit more freedom at the margin it actually strengthens people’s ability and willingness to abide with the major thrust of the restrictions that we still have to ask people in Wales to abide by.
“So by allowing people to go out to exercise more than once a day, by reopening garden centres, by allowing local authorities to begin to prepare for the reopening of libraries, then, we think, that by doing those modest things, it actually helps people to do the bigger things we’re asking of them.
“But, of course, it’s an enormous ask we’re making, and we should all be anxious about how long we can sustain this because by sustaining it there’s other damage being done to people’s sense of mental wellbeing and so on.”
Prime Minister Boris Johnson will announce his plans for the potential easing of any lockdown measures in England on Sunday.
Mr Drakeford said his view was the two countries will be “very much in line with one another.”
“Our new regime won’t come in until Monday so that we move in a timely way together across the United Kingdom, and I still think that that is very much the preferable route.”
Asked about when schools might reopen, Mark Drakeford said he was “not convinced” reopening schools in “any significant way” would be right at this point.
He added: “we’re not going to be reopening schools in Wales during the next three weeks or indeed in June.”
Asked if that meant he was ruling out reopening schools for the whole of June, a spokesman for the first minister said nothing had changed since the education minister’s statement on Thursday which stated schools would not reopen on 1st June.