"We believe that the district court made a wrong decision," Lennart Nilsson told news agency TT. "My client does not at all think that his explanation of the course of events is so improbable as the district court believes and accordingly wants to have a trial in the court of appeal."
The news agency did not give the brothers' names, but the tabloid Expressen has previously identified them as Mensur, 19 and Mentor Alija, 21. They are both Swedish nationals of Kosovar origin.
The deadline for an appeal is August 5th. Mentor Alija's lawyer, Johan Sederholm, confirmed that he will also lodge an appeal on Monday. Deputy chief prosecutor Göran Olsson has not yet decided if he will also appeal.
"I will decide later, before time runs out," he said.
Mensur Alija was sentenced in Helsingborg district court to two years and Mentor Alija three years in prison for attempted arson last week. The crime carries a penalty of two to eight years' imprisonment.
The Alijas, who are from Landskrona in southern Sweden, were arrested in May after two jackets with a driver's license, bank account information and keys to the brothers' home were found outside Vilks' home.
Both brothers have denied their involvement, even though Mensur Alija reportedly suffered serious burns on the night of May 15th, when the attack occurred. He has claimed he was involved in a barbecue accident.
The attack occured three days after Vilks was attacked during a lecture at Uppsala University.
Vilks has faced numerous death threats and a suspected assassination plot since his drawing of the Muslim prophet with the body of a dog was first published by Swedish regional daily Nerikes Allehanda in 2007 to illustrate an editorial on the importance of freedom of expression.
Their publication prompted protests by Muslims in the town of Örebro, west of Stockholm, where the newspaper is based, while Egypt, Iran and Pakistan made formal complaints.
An Al-Qaeda front organisation then offered $100,000 to anyone who murdered Vilks - with a $50,000 bonus if his throat was slit - and $50,000 for the death of Nerikes Allehanda editor-in-chief Ulf Johansson.