In a letter to The Times on Monday, Chope said he did not object to the ban itself but the way it was being introduced.
But he says he'd support moves to make upskirting illegal if it was introduced by the Conservative government.
Gina Martin, an upskirting victim whose petition to criminalise the act won her a legion of celebrity supporters and political backing, said the move left her extremely upset.
Mrs Leadsom said it was meant to secure a second reading in the Commons for the Bill in Government time as soon as possible and certainly before the summer recess, which begins on July 28.
The veteran politician, who was knighted this year, did not explain his reasoning publicly and was not immediately available to Reuters for comment.
Dawn Butler, the main opposition Labour party spokeswoman for women and equalities, said: "What possible reason could there be to block a law that supports women and girls?"
The Bill, which would have progressed to the amendment stage before returning to the Commons and the Lords and, later, receiving Royal Ascent, will have to return for another Friday Private Members Bill session, on July 6, if it is to have any hope of becoming law this Parliamentary term. Only one MP need cry "object" to stop a Private Members' Bill from proceeding, which is why Chose was able to have such unilateral influence.
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There's a new Suzuki Jimny on the way this year, ahead of which Suzuki has released a couple of photos so we know what to expect from the new Jimny.
As MPs returned to Westminster after the weekend, Sir Christopher's parliamentary office was adorned with a string of knickers. "We knew this was a risk-but I now stand with powerful, passionate, women and men behind me".
A 71-year-old Conservative MP who blocked a bill that would have made "upskirting" a criminal offence in the United Kingdom today took a U-turn, asserting that he was not a "pervert" and "wholeheartedly" supports such a law.
The MP for Christchurch said he backed the intent of the bill, and objected to it because he does not support the principle of legislation being passed without debate at second reading.
The first figures on the prevalence of upskirting, published by the Press Association earlier this year, showed complainants as young as 10, with incidents in a slew of public locations such as restaurants and festivals.
Victims said a specific law prohibiting the craze was necessary as current legislation was often insufficient to prosecute an offender.
The practice is illegal in Scotland, where it carries a maximum two-year prison sentence.