Every new teacher in England will be trained in how to spot early warning signs of mental illness, under a plan being unveiled by Theresa May later.
Mrs May, using some of her remaining political authority before leaving office, has called for improvements in preventing problems.
"Too many of us have seen first-hand the devastating consequences of mental illness," says Mrs May.
Labour's Barbara Keeley said the prime minister only offered "warm words".
The shadow minister for mental health said the "reality" was support services being "stretched to breaking point".
Mrs May, having stepped away from debates about Brexit, is using her last days in office to focus on what she sees as key domestic issues.
She wants teacher training to include lessons in identifying children who might have mental health problems and to address issues such as self-harm.
At university level, there will be £1m for a competition to come up with innovative ideas to tackle mental health problems among students.
NHS staff will be encouraged to take suicide prevention training.
The prime minister also promised the publication of a White Paper setting out the government's response to Sir Simon Wessely's review of the Mental Health Act.
Sir Simon will be among those attending a roundtable discussion of his review on Monday, along with Health Secretary Matt Hancock and Simon Stevens, chief executive of NHS England.
The prime minister's efforts were praised by Paul Farmer, chief executive of Mind, the mental health charity.
But Labour's shadow minister for mental health, Barbara Keeley, accused the prime minister of ignoring the "reality" of over-stretched budgets and delays in treatment.
Mrs May, although having stepped down as Conservative party leader, remains as prime minister - and is said to still want to push ahead with ideas and policies that had been held back by Brexit.
Last month she launched the findings of a review into university and further education college funding.
She backed the report's call for a cut in fees to £7,500 in England and an increase in support for further education colleges.
There are believed to be plans for further announcements on education, with suggestions that funding plans to address school and college budget shortages could be brought forward.
Implementation will depend on her successor and the agreement of the Treasury, but Mrs May could still set out her plans for spending more on schools and colleges.
A Number 10 source said suggestions over the prime minister's education spending plans were "speculation".