Charlie Gard, who suffers from a rare genetic condition and brain damage, is unable to breathe unaided. Earlier in the day, parents Chris Gard and Connie Yates said they had expected Great Ormond Street Hospital to end life support for Charlie on Friday.
But hours later, the hospital said in a statement that "together with Charlie's parents we are putting plans in place for his care and to give them more time together as a family."
It's not clear how long life support will be continued for Charlie.
On Tuesday, the parents lost a bid to take Charlie to the US for trial therapy when the European Court of Human Rights sided with earlier rulings that continued treatment would cause "significant harm" and that life support should end.
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Specialists have said the proposed therapy wouldn't help Charlie.
The appeal was the last legal option in the couple's four-month battle. After the final ruling, the hospital said there would be "no rush" to make any changes in Charlie's medical care.
Charlie's case has gained attention online, raising nearly 1.4 million pounds ($1.8 million) on GoFundMe to send him to the US.
Yates has said previously that the funds will be used to support other children with similar genetic disorders should they lose their case.
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