All the nation's 22 councils have been subject to the poll and while all results have not yet been declared, the latest figures show Labour has lost control of Bridgend, which is represented by first minister Mr Jones in the Welsh Assembly, after losing 10 seats there.
The party was also dealt a severe blow in the south Wales valleys, with independents taking control of Blaenau Gwent and the result on a knife edge in Merthyr Tydfil - where the final three seats will be declared on June 8 with Labour needing to win them all to retain a majority.
Labour fared better in other areas retaining overall control of Newport and Neath Port Talbot councils and winning the same number of seats as it held previously on both Wrexham and Flintshire councils, both of which remained under no overall control.
Speaking at Cardiff City Hall where Labour won all of the 15 seats up for grabs in the Cardiff South wards, Welsh Labour and Co-operative MP for Cardiff South and Penarth, Stephen Doughty said he was "really, really pleased" with the results in the area where the party won two seats from Plaid Cymru and one from the Lib Dems.
He said: "There are some strong results coming in from other parts of Wales, mixed results in other areas but I think we can be proud of the campaign we have run here."
A spokeswoman for Plaid Cymru said the loss of Bridgend, where the nationalist party gained two seats, increasing its total there to three, was "quite embarrassing" for Welsh Labour and undermined the status of Mr Jones.
She said: "The concept of Labour safe seats in Wales is rapidly becoming a thing of the past.
"Plaid Cymru is encouraged by the progress we are making in all parts of Wales."
Elsewhere, the Conservatives gained control of Monmouthshire from no overall control and Ceredigion remains under no overall control, with Plaid Cymru retaining its position as the largest party.
Ahead of the election, Labour held 536 seats and had outright control of 10 of the local authorities, but was facing challenges from Plaid Cymru, Tories, Lib Dems and Ukip.
Plaid Cymru had 177 councillors and was fielding 549 candidates, while the Tories held 103 seats and put 621 names on ballots across the country.
Welsh election expert Professor Roger Scully said so far there had been a "much smaller" swing from Labour to Conservative in Wales than in England.
He said: "Labour's worst losses in Wales have been to independents in Wrexham, Merthyr and Blaenau Gwent.
"But Labour held up well in Newport, Cardiff and Swansea."
Labour has retained overall control of Swansea, boosting its majority by winning an extra seat.
Shadow Welsh secretary Christina Rees MP claimed Labour had "defied the pundits" to deliver some strong results across Wales.
She said: "Although there are still results coming in, it's clear from what we know so far that the predicted Tory advance in Wales has simply failed to materialise...
"It's obviously been a difficult night for Welsh Labour in Blaenau Gwent and Merthyr Tydfil, and it's always a blow to lose hard working Welsh Labour councillors."
Ms Rees pointed to Mr Scully's comments on the big picture for Wales and added: "Though many counts are still to take place, the clear message from tonight is large swathes of Wales rejecting the Tories and voting Welsh Labour to stop them from walking all over Wales".
A spokeswoman for the Welsh Conservatives was unwilling to predict what the next few hours might bring.
She said: "We have seen some encouraging results overnight - notably winning control of Monmouthshire County Council - but we take nothing for granted.
"It's too early to give an accurate picture, and we can't assume council results will be repeated at the general election."
Labour has kept control of Cardiff City Council.
Although some results have not yet been declared, Jeremy Corbyn's party has won 38 of the 75 seats.
Plaid Cymru elected councillors in traditional Labour heartlands such as Bridgend and Blaenau Gwent.
Party leader Leanne Wood said: "So far it looks positive for Plaid Cymru, with our stronger areas yet to be announced.
"We have broken new ground in all parts of Wales, from Aberavon to Blaenau Gwent and from Bridgend to Wrexham - the results are all looking positive for Plaid Cymru.
"It's also good to be holding and gaining seats where we have run councils, like in Ceredigion with our strong record on running public services despite the onslaught of cuts.
"People have recognised that, despite facing some of the biggest cuts to our budgets, Plaid Cymru councils have consistently outperformed other councils across Wales and the UK.
"Across Wales there will be more Plaid Cymru councillors defending their communities and standing up to the Tories.
"The story of the night seems to be Plaid and Tory gains versus Labour and Ukip losses.
"I look forward to seeing the results of the remaining counts across the country."