The letter, co-signed by Neil Carmichael (education), Yvette Cooper (home affairs), Sarah Wollaston (health), Iain Wright (business, energy and industrial strategy), and Maria Miller (women and equalities), raises concern at the government's "lacklustre" response this week to a women and equalities committee report into the sexual harassment and sexual abuse of pupils in schools.
That report concluded that compulsory personal, social, health and economic education (PSHE), including up-to-date SRE, was needed to help schools effectively tackle the issue, but the government said it had no intention of forcing all schools to run the lessons.
The letter states that the five chairs "regret that the government's response to that report failed to seize the opportunity of announcing plans to introduce statutory status for PSHE".
The letter adds: "We ask that you give serious thought to this proposal and the benefits that would arise from it.
"We also ask you to consider the consequences of failing to act; not only for the quality of education in England, but also for the lifelong consequences which can result from patchy or inadequate access to PHSE and SRE."
A Private Members' Bill calling for PSHE to be made statutory is currently before the House of Commons and the letter asks Greening to use this as "an opportunity" to reverse the government's stance.
The five committee chairs also wrote to Greening's predecessor Nicky Morgan last January asking her to make PSHE statutory.
Charities and teaching unions have also been highly critical of the government's response to the report by the women and equalities committee.
Russell Hobby, general secretary of the National Association of Head Teachers said: "Yet again we see a parliamentary report call for statutory PSHE.
"Yet again the government's response is to do nothing. PSHE is crucial to provide time in the curriculum to discuss important and sensitive issues, and to protect teachers when grappling with these subjects.
"To tackle sexual harassment and sexual violence, education has to be the key, with good quality age-appropriate sex and relationships education, and PSHE for all pupils."
Lisa Hallgarten, co-ordinator of the Sex Education Forum said that the "case for statutory SRE has been made very powerfully over a number of years and is settled".
"There is abundant evidence that good-quality SRE helps protect children and young people and can positively impact on sexual behaviour; and that current delivery of SRE is patchy and often inadequate to meet the needs of children and young people," she added.
The Department for Education has been contacted for comment.