First Minister Jack McConnell has condemned the attacks on a man and a boy wearing England football shirts.
Ian Smith was wearing an England shirt when attacked
Mr McConnell described the assaults on Ian Smith in Aberdeen and seven-year-old Hugo Clapshaw in Edinburgh as "entirely unacceptable".
Mr McConnell spoke out during First Minister's Questions. Prime Minister Tony Blair made similar comments in the Commons on Wednesday.
Police inquiries are continuing into both attacks.
They are treating the incidents as football-related racist assaults.
Grampian Police said they were disappointed with the response to their first appeal for information about the attack on Mr Smith, 41, who is disabled. He was dragged from his car in Aberdeen and beaten up.
Lothian and Borders Police said they were confident of a result from their inquires into the Hugo Clapshaw incident.
A Grampian Police spokesperson told the BBC Scotland news website on Thursday: "We have had a disappointing response from the public, at that time of day you would have expected quite a few people about.
"We are looking for people to come forward. Somebody must have seen it."
The attacker was described as a man in his early 40s, muscular, 5ft 6in tall, and wore a donkey jacket. He was last seen heading along Clifton Road.
Hugo had been playing with his family in Edinburgh's Inverleith Park on Saturday afternoon when he was punched by a man thought to be aged between 24 and 30.
His father Damon, 34, who was also assaulted, said the attacker was wearing a Rangers top.
A spokesman for Rangers said: "Rangers Football Club was bitterly disappointed to learn of this attack. We have contacted the Clapshaw family to pass on our best wishes to Hugo.
Hugo Clapshaw and his dad Damon were both attacked
"We have also invited him to the Dundee Utd SPL game at Ibrox in early August."
Hugo told BBC Scotland: "I just felt this big whack and I started crying. His eyes looked very fierce."
Lothian and Borders Police described the attack as "cowardly and pathetic".
A spokesperson said: "Inquiries are ongoing. We are fairly confident we will get a result."
Mr McConnell told MSPs at Holyrood: "This is a welcoming country where violent crime has been reducing and our football fans are a source of pride rather than embarrassment.
"But it is entirely unacceptable that any individual of any nationality in this country is attacked because of the football shirts they are wearing.
"And this Parliament sends out a clear message today."
SNP Holyrood leader Nicola Sturgeon said: "I agree with the first minister in condemning the despicable actions of a minority in this country - but also in saying their behaviour should not be allowed to reflect on the reputation of the vast majority of decent people here in Scotland."