During First Minister's Questions in the Scottish Parliament on Thursday, Ms Sturgeon said Somer and Areeb Umeed Bakhsh are a "credit" to the country after MSP Bob Doris raised the Christian family's case.
Ms Sturgeon said she was touched by the Church of Scotland's campaign to keep the boys in the country.
A petition calling on the Home Office not to deport the boys has 85,000 signatures.
She also praised the vicar who has worked hard on their case: "I am really heartened to hear how the community have rallied round the Bakhsh family and about the response to the Rev Pollock's petition.
"I would also like to congratulate Somer and Areeb on what they have achieved in very, very difficult circumstances. "They are an absolute credit to their parents, their school, their community and indeed they are a credit to Scotland. "The Scottish Government will continue to look at what appropriate representations we can make."
15 year-old Somer and 13 year-old Areeb fear they could be killed by Islamic extremists if they are forced to go back to Pakistan.
They boys and their parents moved to Glasgow in 2012 after their father was subjected to death threats from Islamic extremists due to his Christian faith.
The UK Government has repeatedly rejected the family's plea for asylum, largely because officials do not believe they would be at risk in Pakistan.
Ms Sturgeon said there were "deficiencies" within the UK Government's asylum and immigration regime.
"The Scottish Government believes very strongly that asylum seekers must be treated humanely and fairly with their dignity and rights upheld at every stage of the process," she said.
"The Home Office has a duty to ensure that full account is taken of all the individual circumstances in every case and this is particularly important when applications are refused. "And absolutely imperative when children are involved."
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