Lucia Pinochet, the eldest daughter of Chile's former military ruler, has reportedly requested asylum in the US.
Lucia Pinochet was refused entry to the US because of charges in Chile
She was detained at a US airport on an international arrest warrant after fleeing charges of tax evasion and using a false passport in Chile.
Chile's Interior Minister, Francisco Vidal, said he believed her claim would be rejected because "asylum was for cases where there was no state of law".
US officials would not comment on whether Ms Pinochet was seeking asylum.
She was taken into custody on Wednesday after being denied entry at Washington Dulles airport because of the warrant for her arrest.
Chilean and US officials said she was being transferred to an immigration service detention centre while her position was assessed.
Mr Vidal said his government had been officially informed by the US ambassador to Santiago of Ms Pinochet's request for asylum.
"The [Chilean] government rejects that stance," he said. "Chile is a democratic state, a state of law, where all citizens are assured of a just trial."
Ms Pinochet's son, Rodrigo Garcia, told reporters his mother intended to return to Chile to clear her name.
Three of her siblings, her mother and Gen Augusto Pinochet have also been charged with tax fraud in connection with secret foreign bank accounts.
Gen Pinochet's wife was granted bail on Tuesday
The other family members - who deny any wrongdoing - have been granted bail.
Ms Pinochet, 64, arrived in Washington on a flight from Argentina.
She is said to have driven from Chile to Argentina on Sunday, the same day that reports about the possible arrest of the four Pinochet siblings and their mother appeared in the press.
According to the Chilean tax office, Lucia Pinochet has evaded US$859,000 (£480,000) in taxes.
One of Ms Pinochet's brothers, Marco Antonio, described the charges - which also include the use of false passports - as "political persecution" against the Pinochet family.
The investigation into the family's finances began in 2004, after a US Senate probe into Riggs Bank found that Gen Pinochet held secret accounts worth US$8m there.
Further investigations found that the former ruler held more US$26m in foreign accounts.
He is accused of failing to pay nearly US$2.5m in taxes between 1980 and 2004, and is also being investigated for embezzlement of state funds.
The courts have stripped Gen Pinochet of the legal immunity he enjoys as a former president in several cases, including human rights ones, but he has yet to face trial.