Nurul Nasihah was suspended from school last week
"She has been forced to be suspended. I will be consistent with religion. This is my responsibility as a father," her father Faroukh Dawood said, adding that the school gave them until Thursday to change their mind.
Last week two other Muslim girls were suspended for wearing headscarves to class, and another girl stopped going to school after being told to comply with the ban.
International criticism
The row has widened with groups in several neighbouring countries, which have criticised the Singaporean Government's policy of imposing strict uniform codes, which it says helps to maintain racial harmony.
Brunei's only legal political party, the National Solidarity Party (PPKB) said that religious dress did not promote social unrest.
"Religious attires do not contribute to social disharmony and disunity and the wearing of headscarves definitely does not contribute to social disintegration," PPKB President Mohd Hatta Zainal Abidin said in a statement.
Headscarves are compulsory for Brunei's Muslim schoolgirls but not for non-Muslims. Islam is Brunei's official religion.
In Malaysia, several political parties have made similar comments. The spiritual leader of the main Muslim opposition party PAS, said the policy threatened to erode freedom of religion in Singapore.
Race relations
However, Singapore's top Islamic figures have urged the parents of suspended girls to end the standoff with the authorities.
Singapore's Mufti, Syed Isa Semait, said last week that "the no-tudung rule lasts only for a few hours when the pupils are in school".
"Education is more important," he said.
The Islamic Religious Council of Singapore (MUIS) also said the parents should send their girls back to school.
Correspondents say the sensitive issue is testing community cohesion in Singapore, where race relations have come to the fore since the arrests in December of more than a dozen alleged militants suspected of having links with al-Qaeda.
Racial and religious riots broke out in Singapore in the 1950s and '60s. Since then, government policy has focused on avoiding racial and religious tensions between the ethnic Chinese majority and the Malay Muslim minority.
The government says its schools should provide a common space for pupils of all races, religions and backgrounds to mix freely.
For devout Malay Muslims, who make up about 15% of Singapore's population, the tudung is obligatory once girls reach puberty. But some parents insist their daughters wear them from an earlier age.
The headscarf ban does not apply outside schools or to Singapore's private religious schools. But the suspended girls' parents say all the private schools are full.