A target requiring ambulances in England to attend non life-threatening 999 calls within 19 minutes is being scrapped by the government.
In its place, a measure of the "time to treatment" will be introduced.
But the eight-minute response target for life-threatening emergencies will stay.
The GMB union said the changes suggested a "shocking scaling back" of ambulance services, but ministers say they want to focus on quality of care.
The move forms part of a review into the way emergency health services in England are assessed.
A new way of monitoring A&E performance is also to be introduced in April next year to improve the quality of care.
Ministers say the four-hour waiting limit for A&E will be replaced with a set of eight new clinical indicators "that promote quality and patient safety", rather than focus solely on speed.
Time will still be measured as part of the new indicators, but the government stresses that it will "no longer be the only factor".
New indicators will include the number of unplanned re-attendances to A&E and how patients are prioritised for treatment.
The steps are part of Health Secretary Andrew Lansley's drive to move away from what he considers to be the blunt system of targets which have been used in recent years.
Mr Lansley said: "The new measures will focus on quality of care and what matters most to patients - giving a better indication of patient care than the previous process-led targets ever could."
'Not only factor'
He has already relaxed the rules around the 18-week hospital waiting time target and the 48-hour limit to see a GP.
He said he still wanted A&E units to see patients within the four-hour deadline, but added time was not the only factor on which they should be judged.
In total there are eight measures which A&E units will be monitored on from April.
One of those will be to record how long patients have to wait until initial assessment.
Category A ambulance calls, which include the most serious life-threatening conditions, will still need to be responded to in eight minutes.
But the 19-minute target for less serious cases will be changed.
Category B will be replaced with a range of indicators and "time to treatment" times will be published online.
Justin Bowden, national officer of the GMB union, said: "The announcement to scrap the 19-minute response time for ambulances is a shocking scaling back of the service currently provided to the public.
"Andrew Lansley says he knows what matters most to patients but misses what matters most to the public when they dial 999 - that an ambulance arrives, and arrives quickly.
But an NHS spokeswoman said what was actually important in non-emergency cases was how long it took for people to get treated.
The move has been welcomed by doctors who had often complained that the sole focus on the four-hour target distorted priorities.
The coalition had already reduced the threshold for meeting it from 98% to 95% and the hope is that this new focus on other measures will create a new stress on quality.
John Heyworth, president of the College of Emergency Medicine, said: "This is an opportunity to transform emergency care to ensure it becomes the jewel in the crown of the NHS."
The Patients Association said it was important to look at other measures, but added care should be taken to ensure the four-hour limit did not slip too often.
A spokeswoman said: "We do not want to go back to a situation where people are left on trolleys in A&E for days on end."
Professor Matthew Cooke, the NHS's national clinical director for urgent and emergency care, said in reality 90% of what are initially classed as category A calls did not in fact require an emergency response.
But he said the system would err on the side of caution and told BBC Radio 4's Today programme: "If you need an ambulance it will still arrive in a reasonable time, it's just that they won't be rushing to get there in 19 minutes for the nose bleed.
"The other issue behind that is that ambulances rushing through the streets sometimes have accidents and we want to prevent that as well."