The deportation of a promising A-level student to Mauritius must go ahead before she can finish her exams despite a parliamentary committee's appeal for compassion, the immigration minister has said.

James Brokenshire appeared before the Commons home affairs select committee and refused to intervene in Yashika Bageerathi's case, saying it was not sufficiently "exceptional".

Bageerathi's mother, who sat sobbing behind Brokenshire, pleaded for her daughter to be released from Yarl's Wood detention centre. She said it was "not a place for her, it's a place that is cruel".

Supporters of 19-year-old Bageerathi have been campaigning for a reprieve since she was detained on 19 March and threatened with deportation without her mother and two siblings, who live with her in the UK. A petition demanding that she is allowed to stay has collected more than 174,000 signatures.

Lynne Dawes, the headteacher at Bageerathi's school in northLondon, said the teenager had spent two years preparing for the exams and the results were important for her future. Dawes said Bageerathi, who applied for asylum fearing threats of violence if she returned to Mauritius, had voluntarily complied with immigration rules thus far and she thought that was unlikely to change.

MPs asked Brokenshire why it would not be possible to allow Bageerathi – who has been told on two occasions in the last two weeks that she was to be deported, only to be reprieved – to remain in the country long enough to complete her exams in June.

Brokenshire said that although ministers were able to exercise discretion in deportation cases, he felt that this case "did not have the exceptional nature" that would require ministerial intervention. He said he was under an obligation to ensure that Bageerathi was removed from the UK at the earliest opportunity.

The Liberal Democrat MP Julian Huppert said it seemed "perverse to spend a lot of money on treating someone badly". Bageerathi's MP, David Burrowes, drew comparisons between her case and that of the hacker Gary McKinnon, on whose behalf he also campaigned. "What twins these is a sense of compassion and fair play," he said.

Burrowes said Brokenshire had not considered his representations about the case. "What I saw was a predetermined decision having been made. We were concerned in these details that really affect lives that there is proper compassion and fairness. We need to look humanely at every individual case at every point right up to the very end. I don't believe this has happened here."

The committee heard that Bageerathi's age meant she was not covered by deportation rules that protect children sitting examinations. Immigration officials also confirmed that British Airways refused to take Bageerathi on one of its flights as scheduled by the Home Office.