The amount of waste being recycled across Welsh councils hit 60% in the 12 months to the end of March.
Ceredigion was the best-performing authority with a 68% recycling rate and Blaenau Gwent was the worst with 49%.
The target for 2015-16 was 58%, rising to 64% by 2020 and 70% by 2025.
In previous years, fines for councils which did not hit targets were waived but ministers will decide on issuing penalties once final figures are published in October.
The overall recycling rate in the 12 months to March 2015 was 56% as Welsh councils strive to meet the Welsh Government's zero landfill waste target by 2050.
Cabinet Secretary for Environment and Rural Affairs, Lesley Griffiths, said: "This is the first year recycling targets have increased beyond the ambitious level of 58%, up from the previous year's target of 52%. The fact these figures not only achieve the target but, in fact, exceed it is highly encouraging, showing we are continually improving our recycling rate."
"It's clear that local authorities and householders are working hard to recycle and we are well on the way to achieving our 70% recycling target set for 2025. I am proud that we lead the rest of the UK in our recycling rate but I want us to do even better and become Europe's best recycling nation."
Of Wales' 22 councils, only Newport, Blaenau Gwent and Torfaen failed to hit this 58% target in these provisional figures.
Neighbouring councils Monmouthshire and Blaenau Gwent were the only authorities which recorded a drop in recycling rates when compared to their 2014-15 figures.
Monmouthshire fell from 63% to 62% and Blaenau Gwent dropped from 50% to 49%.
However, Monmouthshire recorded a 1% increase when compared to its last 12-month figures, the year to December, whereas Blaenau Gwent remained static in this period.
Protests were held in Blaenau Gwent last year when the council changed bin collections and gave people large plastic boxes for their recycling instead of bags.
The council has defended its position, saying it is still in transition from the old system to the new one.
The Welsh Government said a decision on whether to issue fines to failing councils would be taken in October once final validated figures were available.
Conservative environment spokesman David Melding AM said the overall picture was promising, but added: "There are pockets of Wales and in particular the south east, where recycling rates remain stubbornly low and that requires investigation from the Welsh Government."
Caerphilly council, one of the local authorities which struggled to meet the 56% recycling target previously, saw its rates hit 62%, up from 59% in the 2015 calendar year.
In a bid to tackle the problem, the authority is visiting every home in the county to encourage uptake.
It is halfway through the visiting process and said so far, most people were responding positively to the advice.
Colette Price is one of the Caerphilly team visiting the council's 74,000 homes.
She will hand out free replacement food waste bins if people do not have one already, give advice and leaflets about what can be recycled and when it is collected and ask if they have any issues.
She said: "I like to go down the route of trying to encourage, not boss them and say 'you've got to do this, you've got to do that'.
"I think it's important that the residents know that we are there to inform them and if they've got any issues there is a telephone number on the leaflet, and they can contact us."