Wrexham is the most expensive place for a burial with fees topping £4,000, while Pontypridd, Rhondda Cynon Taff is the cheapest at £3,269.
Aberdare, Rhondda Cynon Taff is the most expensive place for a cremation, costing an average of £3,353.
A cremation in Cardiff is the cheapest in Wales costing an average of £3,144.
A basic funeral includes collection and care of the deceased, a basic coffin, a hearse, a simple service and a burial or cremation.
Additional items like flowers, funeral cars and ministerial fees are not included.
Wales has seen a rise of 5.2% - the biggest in the UK. In Scotland the average cost rose by just 2.4%
The Royal London National Funeral Cost Index figures are only available for towns and cities where both cremations and burials are available.
Simon Cox, a funeral cost expert at Royal London, said: "The rising cost of an average UK funeral is very concerning. It has outstripped inflation considerably for many years - almost in line with house price rises, which as we know continue to rise rapidly as demand outstrips supply."
He added: "The UK funeral system still displays fundamental failings, which we reported last year. Vulnerable bereaved people are taking on increased debt; and we predict this problem will worsen if steps are not taken to tackle the many, persistent causes driving up the cost of funerals."
The average cost of a funeral in Wales has risen by £170 to £3,461 over the past year, figures have shown.