Airports in Liverpool, Manchester and Bristol are also still closed.
Cardiff Airport's business development director Steve Hodges said: "I'm afraid it's going to be another difficult and disappointing day for passengers across the UK.
"We are going to lose 50 flights again today, another 3,000 passengers plus those who were re-booked yesterday which must be intensely frustrating for them."
He said the airport could "only apologise" but the cancellations were due to "extraordinary circumstances" and he asked those due to travel for their patience.
"Safety has to be paramount," he added.
"There is plenty of evidence of the impact dust can have on engines and I'm sure most people are now aware of that."
A Stena spokesman said there had been a "significant" rise in ferry passengers because of the airline problem, while Irish Ferries said inquiries for reservations had quadrupled compared to the usual volume of calls.
"We are filling ships which is what we wouldn't normally do this time of year," said Stena spokesman Eamonn Hewitt.
"There is a lot of demand from foot passengers, they are just showing up at the ports."
Phil Jones, chief executive of the Swansea-Cork ferry operator Fastnet Line, said there had been an "uplift" in bookings.
The airport said over 3,000 passengers would be affected on Friday
Arriva Trains Wales said it was experiencing increased demand for services as air passengers switched to ferries and trains for travel between the UK and Ireland.
Extra capacity is being added to train services to and from Fishguard Harbour in Pembrokeshire and Holyhead on Anglesey.
A Nats statement said: "The cloud of volcanic ash continues to cover much of the UK and the eruption in Iceland continues."
Nats said a limited number of flights could run to and from Northern Ireland and parts of Scotland.
Ten chefs from the Welsh national culinary team who are due to compete in a competition in Singapore have been affected by the disruption.
The chefs have spent months preparing for the culinary event, which is due to start on Tuesday, but their flight from Manchester was cancelled.
On Thursday, a flight returning the body of a Swansea soldier killed in Afghanistan landed early to avoid being grounded.
Fusilier Jonathan Burgess, 20, of 1st Battalion The Royal Welsh, was killed in Helmand province last week.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.