A British couple who feared a $200,000 (£130,000) medical bill after their baby was born 11 weeks premature while they were on vacation in New York breathed a little easier on Friday as the hospital caring for their son said it would “ensure that there will be no financial impact to the family”.

Katie Amos and Lee Johnston’s baby, Dax, reportedly born weighing 3lbs, is in the neonatal intensive care unit at Lenox Hill hospital in Manhattan.

On Friday, a hospital statement said: “Lenox Hill Hospital continues to work with the insurance carrier regarding payment approvals for all services rendered by the hospital, anesthesia and physician services from their insurance carrier. We will ensure that there will be no financial impact to the family.

“In addition, our staff has been going above and beyond to ease the overall experience for the family, from arranging a place to live for the duration of their stay to helping them communicate with their family in the UK.”

By Friday afternoon a fundraising page – started in an effort to help Amos and Johnston – entitled “Dax’s Tale of New York” had raised $9,577.68 (£6,248).

Earlier, the couple’s friend Richard Crow wrote on a Facebook page of the same name: “Great news! I believe I can confirm that all medical bills will be covered! It’s been a long wait but well worth it! Due to the publicity that has gone on around the whole story, it has forced them to pay!”

The Facebook page had garnered more than 13,600 likes.

Amos and Johnston, from Lincolnshire, said they were told by doctors their bill could reach $200,000, as they would have to stay in hospital until 10 March, when Dax would be cleared to travel to the UK. The baby was reportedly born 28 December. Crow said he started the fundraising page because people wanted a way to help the young couple out. He said Johnston and Amos had not asked him to do so.

“I am running it. Neither Lee [nor] Katie have asked for any money”, he wrote.

“Myself and a few good friends got together to see what we could do to help them. It was only really to be a local thing. It was decided we would start a FB page and I said I would run it. It was also my decision to do the page as baby Dax.”

Crow’s efforts attracted significant publicity, including support from the British model Katie Price.

Crow said the money raised would be used to support the couple during their extended stay in New York, as Johnston is self-employed and Amos receives only basic maternity pay. He said an airline had agreed to honor the couple’s return flight to the UK when they were ready to leave New York.

Crow said the new parents would donate any remaining money to the Ronald McDonald Fund, which has provided temporary housing while Dax is in hospital. He also offered donors the chance to ask for their money back if they felt “cheated” or if they had misunderstood the situation – he said the fundraising effort had not been intended to reach the $200,000 figure quoted for the couple’s medical bills.

The couple did not have travel insurance, but had received clearance from their doctor to fly, Crow said, before they undertook their five-day trip to New York. Dax was born after Amos went into labour during a movie tour of Central Park. Crow said both parents and Dax were well and immensely grateful for the support.

“Dax is doing fine,” Crow wrote on Facebook. “Lee got to feed him yesterday for the first time, though I understand it is an [unconventional] task!!! They seem in better spirits now due to … the support back here.”