A letter from Petitions Committee chairman William Powell to the education minister said there was widespread confusion over the policy.
The committee is investigating after thousands of complaints from parents.
It comes as figures show the number of fines varies between councils.
A BBC Wales Freedom of Information request found Cardiff council issued 370 fixed penalty notices between January and May.
During the same period, 10 other councils, including Monmouthshire which has not yet introduced fines, did not issue any.
In his letter to Huw Lewis, Mr Powell said the committee was concerned many councils were incorrectly advising schools only to authorise term-time holidays in "exceptional" circumstances, with some asking head teachers not to authorise any at all.
Speaking on the issue, before the letter, Mr Powell said: "The relationship between parents and schools is absolutely crucial and I think it's potentially very damaging to have this rather aggressive approach being brought in.
"We need to have a degree more common sense."
The Welsh government has said parents do not have an "automatic right to withdraw pupils from school for a holiday and they must apply for permission in advance".
But it does give schools "discretionary power to authorise up to 10 days absence during a school year for family holidays during term time".
Two campaign groups have drawn up petitions calling for children to be allowed term-time holidays. The largest petition, with 18,000 signatures, is from a group called Let Children in Wales Have a Family Holiday During Term-Time. The other petition has been drawn up by Pembrokeshire Parents Want a Say.
Campaigner Bethany Walpole-Wroe, from Llanybydder, Carmarthenshire, said many families could not afford to go away during school holidays.
"The prices more than double usually in July and August, so they either can't afford them or they can't get time off due to various circumstances," she said.
But the Welsh government said school attendance should come first.
Education Minister Huw Lewis said: "Prolonged absence from school really does damage the attainment prospects of young people and that's why I, and I think most parents, would put learning as a priority."
Head teachers' union National Association of Head Teachers (NAHT) Cymru said while everything possible should be done to ensure children have the least amount of time out of school, it would not encourage its members to fine parents.
Campaigners will find out in the new year if the committee intends taking any action.

Voges was forced to retire hurt on 86 after suffering the injury while batting during the County Championship draw with Somerset on 4 June.
Middlesex hope to have the Australian back for their T20 Blast game against Hampshire at Lord's on 3 August.
The 37-year-old has scored 230 runs in four first-class games this season at an average of 57.50.
"Losing Adam is naturally a blow as he contributes significantly to everything we do," director of cricket Angus Fraser said.
"His absence, however, does give opportunities to other players who are desperate to play in the first XI.
"In the past we have coped well without an overseas player and I expect us to do so now."
Defending county champions Middlesex are sixth in the Division One table, having drawn all four of their matches this season.
Voges retired from international cricket in February with a Test batting average of 61.87 from 31 innings, second only to Australian great Sir Donald Bradman's career average of 99.94 from 52 Tests.

The former Ireland head coach, 53, had endured a difficult time since taking charge in April last year.
A year ago, he was suspended and then reinstated following comments he made about team selection.
Joel Garner, Henderson Springer and Roddy Estwick will lead the team when they face Pakistan in three T20s, three ODIs and three Tests in the UAE.
The first match - a T20 game - takes place on 23 September in Dubai.
The West Indies Cricket Board (WICB) cited "differences in culture and strategic approach" with Simmons.
The former all-rounder had questioned the omission of all-rounders Dwayne Bravo and Kieron Pollard from the one-day squad last year.
He was suspended by the WICB, who said Simmons had appeared to "question the legitimacy of the selection process".
The departure of Simmons follows the sacking of Curtly Ambrose as bowling coach and Darren Sammy as T20 captain.
West Indies are currently third in the world T20 rankings but lie eighth in both Tests and one-day internationals respectively.
Some parents who have been fined for taking holidays in term-time may have been dealt with unfairly and unlawfully, an assembly member has claimed.
[NEXT_CONCEPT]
Middlesex batsman Adam Voges will be out until August after suffering a torn calf muscle in his right leg.
[NEXT_CONCEPT]
Phil Simmons has been sacked as West Indies coach just five months after their stunning World T20 triumph.