A total of 1,860 ambulance calls over three winter months took longer than six hours to respond to, figures show.
Statistics released to the Welsh Conservatives show the waits patients have faced when their calls are classed as amber - deemed not immediately life-threatening.
The party described the response times as "shocking".
But the Welsh Ambulance Service says the figures need to be set against the backdrop of sustained winter demand.
A spokesman for the Welsh Government said targets for the most serious calls were being exceeded.
The figures for December 2017 to February 2018 come after what had been described as the "busiest winter on record" for the Welsh NHS by Health Secretary Vaughan Gething. They do not include the cold snap in March.
According to statistics obtained under the Freedom of Information Act by the Welsh Conservatives, 34,768 of 68,186 calls (51%) classed as amber during the period took longer than 30 minutes.
A total of 5,706 took longer than three hours, while 1,860 took more than six hours.
Ambulance calls in Wales are given three categories - red, amber and green - under a system introduced in 2015 that saw response time targets scrapped for all but life-threatening calls.
The most serious and life-threatening calls are classed as red, with paramedics expected to reach 65% of such patients within eight minutes.
Calls that are also serious but not immediately life-threatening are classed as amber - including chest pains and strokes.
The Welsh Government has said patients will receive a fast, blue light response but there are no targets for how long amber calls should take.
In December a wait of 54 hours for an amber call was recorded in the Aneurin Bevan Health Board area - although the ambulance service said the individual was in hospital and had been waiting for a transfer for specialised treatment.
A wait of 43 hours was recorded in the Abertawe Bro Morgannwg health board area in February.
Welsh Conservative leader Andrew RT Davies said some of the figures were "horrendous".
"There are huge pressures on the health service - we understand that," he said.
"But the management of the health service from this current health secretary leaves a lot to be desired.
"These figures for the ambulance service lay bare the desperate situation of many of our paramedics and other health workers find themselves in - leave alone the patients."
Former Welsh Ambulance Service regional director Dafydd Jones Morris thinks politicians should "allow a rethink" in the service's deployment priorities and demand more funding.
"They require more resources to deal with the less immediate calls with a different type of staff, but with trained people rather than relying on volunteers to attend," he told BBC Radio Wales.
"Targets have been rethought three times in the last six years and its about time they did it again because there is something fundamentally wrong in having so many people having to wait so long for an ambulance."
Over the same period, 70% of 6,375 red calls were responded to in the target time of eight minutes.
A total of 20 red calls took longer than half an hour, while one, in January in the Betsi Cadwaladr health board region in North Wales, took 90 minutes to respond to.
But the Welsh Government said the Welsh Ambulance Service had exceeded the national target for red calls for 29 consecutive months, with an average response time of around five minutes.
A Welsh Ambulance Service spokesman said: "In terms of the figures for amber calls, which include a range of conditions from those which are serious but not immediately life-threatening, to those which are painful but less severe, such as broken bones, these need to be set against the backdrop of sustained demand across the winter period."
He said cases of more than six hours represent "just 2.1% of the total number of incidents we attended".
"Given the sustained increase in demand across the system, with many poorly patients in need of our help, it is inevitable that some people will, unfortunately, have to wait longer."
He added: "No-one at the Welsh Ambulance Service, or indeed across NHS Wales, is complacent about providing the best possible levels of service and care to the people we serve, and we will continue to work as a system to improve what we do."