Face masks outdoors will be obligatory only if social distancing cannot be kept, the minister said at the government's coronavirus briefing on Friday.
National sports competitions will be relaxed for younger athletes, contactless outdoor recreation for up to 10 people will be allowed, and ski resorts will reopen.
Museums, libraries and galleries will also reopen, and one-to-one classes at music schools and ballet classes will be allowed.
Some more shops, and services such as hairdressers and car repair shops will reopen.
While all kindergarten and primary school children will be in in-person learning, secondary schools will teach under model C, meaning pupils in the first first three years come to school every other week, while last-year pupils are at school.
This is a relaxation since this model previously kicked in as part of the more favourable stage orange. Mateja Logar, head of the Covid-19 advisory team, said this was to keep kids in school.
While the strict 1-11 April lockdown is being relaxed, the country is well in the third wave of the epidemic, whose extent is difficult to fully predict, said Poklukar.
The government will thus formally extend the epidemic by another 30 days, he said.
"We are currently at the point of transition from tier orange to red, which we are expected to reach next week. The third wave has not yet culminated.
"In the coming weeks we will be adjusting decisions according to the situation by regions," said Poklukar, who said the April lockdown helped prevent tier black.
NIJZ director Milan Krek said that by Tuesday the entire country will be red-coloured, with some regions possibly already in tier black.
Red stage means the seven-day average of new daily infections is below 1,350, and hospitalisations are below 1,200.
Poklukar, Krek and Logar thus urged residents to strictly abide by all the precautionary measures.
Under the overhauled traffic-light strategy, tier orange will imply lifting the ban to move between regions, allowing outdoor hospitality and some more in-person teaching at higher education establishments.
Tourist companies will reopen in tier yellow, when secondary schools and higher education establishments will fully reopen.
Lagar said the advisory team was aware residents were tired of the restrictions, but this was the only way for health workers to avoid "hard decisions" in case of a worsening.
Poklukar also commented on the Constitutional Court staying a provision which restricts travel to countries on Slovenia's red list of high-risk countries, pending its final decision.
Given the court's decision, the same rules as before the 1-11 April lockdown would now apply: a negative PCR test from an EU country for all but the few exceptions, including daily commuters and children going to bilingual schools.
