The FA Cup semi-final between Arsenal and Blackburn will take place on Saturday, 16 April with Manchester United facing Newcastle the day after.
Both games will be staged at Cardiff's Millennium Stadium, with the first match kicking off at 1215 BST and the Sunday game starting at 1400 BST.
Man Utd had asked for their game to be moved closer to the north of England.
But FA spokesman Adrian Bevington said: "We announced Cardiff as the venue last year and it's proved very popular."
Bevington added: "The kick-off times are always set after full consultation with the police and other safety authorities, and with safety and security considerations given the highest importance.
"We have taken a responsible decision bearing in mind these issues and the travel arrangements for fans from the four competing clubs."
On Monday, the Independent Manchester United Supporters Association chairman Jules Spencer, said his association would not back down from their stance against the plans.
"IMUSA would never seek to tell United supporters what to do," he said.
"We all have to make a personal choice, as members of our organisation have done, between the desire to support the team and the hassle, cost and inconvenience the FA are forcing us into by travelling to Cardiff.
"We are re-iterating our belief that the game should be switched to Elland Road and we will be doing everything in our power to make this happen."