Kirsty Williams told a press conference in Cardiff that her “preference” would be for all children to return after the holidays, which begin on March 29, with the new term starting on April 12.
The youngest pupils, aged three to seven, began returning to face-to-face teaching from Monday along with some vocational learners who were back at college.
Most children have not been in school since December, when classes were switched online due to a steep rise in coronavirus cases.
The coronavirus incidence rate in Wales is currently 80 cases per 100,000 people – the lowest of the four UK nations.
All primary school pupils, as well as those in years 11 and 13 and those doing similar qualifications in colleges, will return from March 15 if the situation continues to improve.
Ms Williams said she wanted to see other learners, such as years 10 and 12, have “flexibility” around face-to-face teaching.
“Unfortunately for those learners in secondary settings or colleges, this won’t necessarily be a return to full-time on-site learning,” she said.
“However, we will do all that we can to support those learners because I know how anxious this time can be as they consider key decisions about their next steps in life.
“Last time I spoke at the press conference, I announced how our education staff will be tested twice weekly as part of our testing strategy.
“Today, I’m pleased to say that this will be extended to older year learners in years 11 to 13, and those in further education (FE) settings.
“This testing will be done through lateral flow devices, which mean they can be done from a learner’s home and which will assist with the planned returned for older pupils from March 15.”
Ms Williams stressed that educational premises were safe but the movement around them contributed to the R number, which is currently estimated to be between 0.6 and 0.9 in Wales.
She called on pupils, parents and carers to follow guidance and restrict contact with others to ensure that more children could return to school.
“We will confirm the situation for other learners before the Easter holidays but I can tell you now that my preference is to get all learners back in school after the break.”
She added: “My preference is to get all children back to face-to-face teaching after Easter but whether the virus will allow us to do that, of course, is a different thing.
“Rather than just focusing on dates, we will be focusing on what the public health situation allows us to do.”
