Linsey Farnsworth, Labour MP for Amber Valley, said: "Although I'm expecting that the government's position will be that they wouldn't be accepting two weeks of holidays for school children, I think it's clear from what Natalie has said that this isn't just about parents wanting to take children on holiday during term time.
"There's a lot more complexity to this and a lot more issues.
"And I think it's fair to say that there are instances where the current system does provide some injustices for people."
She said Ms Elliott's petition was "a phenomenal piece of work" and said the current system was "a bit of a postcode lottery for some in terms of different schools applying the rules in a different way and different outcomes therefore as a consequence".
A Department for Education spokesperson said: "Through our Plan for Change, we're determined to give children growing up in our country the best start in life.
"But that can only happen if a strong foundation for learning is built through children regularly attending school.
"We have already made significant progress with five million more days in school last academic year and 140,000 fewer pupils persistently absent.
"Poor attendance damages children's prospects and term time holidays place the burden on teachers to support missed learning – affecting the entire class.
"That's why fines have a vital place in our system, so everyone is held accountable for ensuring our children are in school."