The older brother, who is understood to be 35 and from Lithuania, was ordered to remain locked up by the Göta Court of Appeal on Tuesday morning, while police continue to investigate the case.
Both men were arrested just over a week ago after Lisa Holm's body was found following the largest volunteer search for a missing person in Swedish history. They deny killing the schoolgirl.
Swedish rules allow suspects under “strong suspicion” to be held for up to a fortnight, with room for the period to be extended further after that.
Later on Tuesday the court also remanded the younger suspect, 31, in police custody.
The older brother's lawyer Inger Rönnbäck told the TT news agency that they would appeal the decision to Sweden's Supreme Court, the highest court in the country.
“My client is obviously very disappointed. He is determined in his denial and we want the Supreme Court to look at the evidence which we believe is thin and lacking,” she said.
However a woman accused of “harbouring a criminal” in connection with the case has been released.
Deputy Chief Prosecutor Lars-Göran Wennerholm told TT: “I've had a week to strengthen the evidence and I have not succeeded”.
Lisa Holm disappeared after working a shift at a cafe on June 7th in Lidköping, a small town in a rural area north east of Gothenburg, close to two of Sweden's largest lakes.
Around 900 volunteers joined the hunt for the teenager, searching woodland, fields and buildings in the region.
Police said on Tuesday that cordons around all of the suspects' homes had been lifted.