For two months, the Tamrazyan family have been sheltering at the Bethel church in The Hague, which has taken advantage of a Dutch law that authorities cannot enter while a service is underway.
The church said junior justice minister Mark Harbers had on Thursday informed them of the "harsh and unjust" decision "not to use his discretionary jurisdiction to grant the Tamrazyan family permits of residence".
The church "cannot accept the rejection and will continue" to give the family refuge there, it said in a statement.
Theo Hettema, chair of The Hague Protestant Church, added: "Just before Christmas, when we celebrate God's humanity-loving and peaceful deeds, we feel strengthened not to forsake our responsibility for the Tamrazyan family."
The family fled Armenia after the father received death threats for his political activities and have been living in the Netherlands for nearly nine years.
Eldest daughter Hayarpi Tamrazyan, 21, who has effectively become the spokesperson for the family, her mother, father, 19-year-old sister and 14-year-old brother took refuge in the church on October 25 after Dutch authorities turned down their request for asylum.
The Dutch justice ministry has the power to exceptionally grant asylum to minors who are subject to expulsion orders -- known as a kinderpardon.
A justice ministry spokesman told AFP that Harbers had said he would not use the discretionary power, confirming an earlier decision on the matter. The ministry had informed the family on Thursday, the spokesperson added.
Nearly 650 pastors from the Netherlands and other countries have been praying 24/7 to exploit the loophole in Dutch law which says authorities cannot enter if a religious service is going on.
The government had ignored an "extensive file with new information" on the family's cause presented by the church-related refugee organisation INLIA, the church statement said.
"The grounds on which the secretary of state has put aside this file are so disputable that the church has no other option but to continue with the church asylum."
The case has put the church and the family under the media spotlight.
Hayarpi Tamrazyan told foreign media on December 13: "I really don't know what the outcome will be but we hope we can stay here because this is our home, this is where we belong."