In her first comments to the House of Commons since leaving the Cabinet on Monday, Ms Greening also called for cross-party support for changes to the guidance for teaching RSE in primary and secondary schools.
Addressing a parliamentary question to home secretary Amber Rudd, who took over Ms Greening’s brief as minister for women and equalities in the Cabinet reshuffle this week, Ms Greening said: "First of all I'd like to congratulate the home secretary on her expanded role – I know she will do a brilliant job.
“And she will know that young people, parents and teachers think it's vital in a modern, internet world to see sex and relationships education updated.
"Can she confirm that the government will push ahead with updating the guidance that's now so out of date, but also if she will meet with myself, [Maria Miller, chair of the women and equalities select committee] and also [shadow women and equalities minister Sarah Champion] to make sure we can have a cross-party support for the work that is being undertaken?”
Ms Rudd confirmed that she would be “delighted to work with [Ms Greening] to ensure that that is the case, and also across the House to ensure that the outcome we get is one that the whole House can support”.
Earlier this year, legislation passed by Parliament made relationships education compulsory in all primary schools, and relationships and sex education compulsory in all secondaries.
Last month, the government launched an eight-week consultation, asking teachers, pupils and parents to offer their views on what kinds of RSE lessons would be appropriate for different age groups.
The evidence given during this consultation will be used to help develop RSE curriculum guidance that is relevant to the modern world.
Existing guidance was last updated in 2000. As a result, it does not address risks to pupils such as sexting, online grooming and pornography.