AMSTERDAM (Reuters) - A round-the-clock prayer service to stop an Armenian family being deported from the Netherlands was ended after 96 days on Wednesday, after the government agreed to make an exception to immigration rules.

Using a law that bars police from entering a place of worship while a service is in progress, hundreds of supporters of the Tamrazyan family have held rites non-stop at the Bethel church in The Hague since Oct. 26 to block their deportation.

Late on Tuesday, the cabinet decided to allow the Tamrazyans and other families rejected for permanent residence after living for years in the Netherlands to stay in the country after all.

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The families, which together have around 700 children, did not qualify for an exemption granted to minors living in the Netherlands for more than five years.

To avoid other families with no other prospect of qualifying for permanent residence taking root in the Netherlands, the government will also try to speed up asylum procedures.

"We are incredibly grateful that hundreds of refugee families will have a safe future in the Netherlands," a spokesman for Bethel Church, Theo Hettema, said on Wednesday.

But he said the church was worried about the consequences for future immigration policy.

The fight over the "children's pardon" put pressure on Prime Minister Mark Rutte's centre-right government, which has only a one-seat majority in parliament's Lower House, and looks set to lose its Senate majority in a March 20 election.

Rutte's Liberal party is trying to present a tough stance on immigration, to avoid losing ground to opposition parties such as the anti-Islam party of Geert Wilders.

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Although Tuesday's decision was good news for the Tamrazyans, it came days too late for another family, the Grigoryans. That family of five, with children aged three to eight, was deported to Armenia early last week, just as the cabinet began deliberating on the issue.

"This is unfair and very painful," their lawyer told Dutch news agency ANP on Wednesday.

"If their deportation had been postponed a few days, the family would have been allowed to stay."

(Reporting by Bart Meijer; Editing by Catherine Evans)