Drivers face being given six penalty points on their licence rather than three, and a Â£200 fine instead of Â£100.
But figures obtained by BBC Radio Wales showed 166 motorists were stopped by police for using their phones in March - up from 137 in February.
The Handsoff campaign said driving and using a phone is a "lethal cocktail".
The changes to the law, introduced on 1 March, mean new drivers caught using a mobile phone face losing their licence, and more experienced drivers can be banned if they get 12 points in three years.
Lucy Amos, from road safety charity Brake, said: "Mobile phone use behind the wheel is a growing menace and it's time we got tough with those who break the law.
"These drivers are putting their own and other people's lives in grave danger.
"As a charity that supports bereaved and seriously injured road crash victims we know only too well the devastation and heartbreak caused by distracted drivers and have been campaigning on this issue for a number of years.
"We would also like to see a total ban on phone use as even using hands-free increases your likelihood of being involved in a crash. It's the distraction of the conversation that's the main danger."
She added mobile phone use should be as big a taboo as drink driving.
A spokesman for Mobile UK, the trade association for the UK's mobile operators, told the Jason Mohammad programme the UK government had been taking the lead on action to tackle the issue.
"Mobile UK and mobile operators have been supportive of the measures that respective governments have been doing to reduce hand-held mobile phone use in vehicles but government have very much been taking the lead," he said.
BBC Wales also contacted mobile phone networks EE, Vodafone, O2 and Three.
A spokesman for Vodafone said: "Mobiles and driving don't go together... texting while driving is never acceptable."

The Music Group said a consultation on redundancies at its Tannoy loudspeaker production facility in Coatbridge began on Tuesday.
The consultation will last for at least 30 days, according to the company.
Production of audio equipment at the plant is understood to be moving to China.
Tannoy is one of the oldest audio brands in the world, having been founded as the Tulsemere Manufacturing Company in 1926.
It has had a base in Coatbridge since the 1970s.
The company remains active in a range of audio sectors including residential hi-fi and studio monitoring.
Peter Sommer, senior vice president of lifestyle at The Music Group, said: "I can confirm that Music does propose to dismiss as redundant around 70 staff at its manufacturing and office facility in Coatbridge.
"However, I would emphasize that no final decision has been taken in relation to these proposals, which are the subject of a detailed collective consultation process which began on Tuesday 3 May 2016 and which will last for at least 30 days and possibly more.
"In the event that the proposed dismissals are ultimately confirmed following the conclusion of the consultation process, the Coatbridge facility would cease operations and the plant would close.
"Given that the proposals are at a formative stage, there is of course no definitive time scale in place, but it is envisaged that any closure would likely be towards the end of the year."
He added: "Music is of course mindful of its obligation to seek out any suitable alternative employment for any employees whom it is confirmed are to be made redundant, and to that end the company will be doing all that it can to try to identify any suitable alternative roles which may exist in any of its operations in Europe and beyond."
Mick Conroy, GMB Scotland senior officer, said: "In the year of Tannoy's 90th anniversary, it's an absolute tragedy that the long-serving Coatbridge workforce has been rewarded with the sack.
"These latest redundancies also show the total free-fall in Scotland's manufacturing sector as our slide towards a low-skill, low-wage and precarious economy gathers apace without any intervention.
"A key priority of the next Scottish government must be to address our manufacturing crisis by bringing forward a meaningful industrial strategy that can help steer our economy back towards growth."
The number of Welsh motorists caught using their mobile phones went up in March, despite the introduction of harsher penalties.
[NEXT_CONCEPT]
The owners of an audio manufacturing factory in North Lanarkshire have confirmed that the plant is facing closure, with the loss of 70 jobs.