In the thousands of texts, Mr Griffiths asked the women to send him explicit photos and videos and is also reported to have offered to rent a flat to meet the pair for sex.
Describing himself as “embarrassed” and “deeply ashamed” at his actions, the Burton MP has resigned as a Minister in the Department for Business, Energy & Industrial Strategy.
In a statement he said: “I am deeply ashamed at my behaviour which has caused untold distress to my wife and family, to whom I owe everything, and deep embarrassment to the Prime Minister and the Government I am so proud to serve.”
He went on the apologise to his local Conservative Party and to his constituents in Burton.
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He added: “I do not seek to excuse my behaviour and will be seeking professional help to ensure it never happens again.
“In time I hope to earn the forgiveness of all those who put their trust in me and that I have let down so terribly.”
Mr Griffiths was formerly Theresa May’s chief of staff.
The MP is understood to have sent the masses of messages over a period of just three weeks after he became friendly with the paid on social media.
May thanks Davis and Johnson after their resignations 1769452610ebxV9d1m
The crude texts included messages such as: “I’m going to need something filthy to put a smile on my face. I want to see you both naked.”
Another read: “I’m thinking maybe we need a flat for Daddy’s girls. I’m taken by you both. You girls are spectacular.”
He also bragged to the women that he was powerful in politics and referred to himself as “daddy” in multiple texts.
In one example he said: “Daddy’s busy running the country.”
The Tory has previously been a vocal advocate of increasing the number of female MPs and improving the number of women in boardrooms.
His resignations likely to come as a major blow to Mrs May as it makes Mr Griffiths the Prime Minister’s sixth resignation in a week.
David Davis and Boris Johnson both quit the Cabinet this week in protest at Mrs May’s Brexit negotiation stance.
They argued the Conservative leader’s plan would fail to properly honour the result of the 2016 EU referendum.