Encouraging teachers in England to stay in the profession will "remain a significant challenge" for the coming years, a committee of MPs stresses.
The Education Select Committee says the next government will have to ensure recruitment targets are improved.
The government says it is committed to addressing the challenges schools face.
The Department for Education said it had committed to spending over £1.3bn on attracting new teachers into the profession up until 2020.
In a report published in February, the cross-party group of MPs had accused ministers of failing to take adequate measures to tackle teacher shortages.
In response to the MPs' report, the DfE said overall teacher retention rates had remained broadly stable for the past 20 years, and around seven out of 10 teachers remain in teaching five years after qualifying.
The DfE said it recognised that "significant challenges" remain, but added: "The government is committed to doing whatever it can, working closely with the profession as a whole, to ensure that every pupil in England's schools is taught by excellent teachers."
Commenting on the DfE's response to its February report, committee chair Neil Carmichael said the issue of teacher recruitment and retention would remain a problem for the foreseeable future.
He said: "The problems of recruiting and retaining teachers will remain a significant challenge for schools over the coming years and the government will need to focus on helping to tackle issues such as teacher workload and access to continuing professional development.
"The next government should set out clearly how it will encourage teachers to stay in the profession and ensure recruitment targets are improved."
Pupils' mental health
In a separate report, the Education Select Committee and the Health Select Committee found schools and colleges in England were struggling to provide adequate time and resources for pupils' well-being.
The MPs said financial pressures were putting a squeeze on the provision of mental health services, such as in-school counsellors, at a time when there was growing concern about young people's mental health.
In a joint inquiry into children and young people's mental health, they found that half of all cases of mental illness in adult life started before the age of 15, and that one in 10 children aged between five and 16 have received a diagnosed mental disorder.
The MPs call for changes in the curriculum and ongoing work with teachers and support staff to be made part of a drive across schools and colleges to promote well-being.
Social media providers should be more alert to the dangers of harmful content, and too much social media use is linked to sleep deprivation and depression in youngsters, they said.
Dr Sarah Wollaston, chair of the Commons Health Committee, said: "With half of all mental illness starting before the age of 15, and three quarters by aged 18, the government and educators must ensure sufficient time is allowed for activities in schools and colleges that develop the life-long skills children and young people need to support their well-being."
Mr Carmichael added: "Schools and colleges must be well-resourced to provide on-site support and make referrals where necessary."
Geoff Barton, general secretary of the Association of School and College Leaders, said the MPs' findings reflected its recent survey of school leaders.
ASCL found that half of respondents had cut back on mental health support services for students, such as counselling and educational psychologists, as a result of a squeeze on budgets.
Mr Barton said: "The impact on mental health support is particularly concerning at a time when the incidence of mental health problems among young people is increasing.
"School and college counsellors play an important role in identifying problems and providing support at an early stage, referring young people to specialist local mental health services where necessary.
"Unfortunately, these services are also severely underfunded and there are significant gaps in this provision in many areas."