A Syrian refugee family whose home in Merseyside was firebombed in the middle of the night are “overwhelmed and thankful” for the outpouring of support, a charity helping them has said.

The family of five were forced to flee their home in St Helens when it was set alight as they slept in the early hours of Sunday, police said.

The family – a pregnant woman, a man and their three children, aged two, three and five – suffered from smoke inhalation and had to be rescued from the property by neighbours.

Detectives were investigating whether the arson attack was a hate crime, a spokesman for Merseyside police said on Thursday. The perpetrators have not yet been caught.

The young family had been living in St Helens since January after arriving in the UK under the government’s Syrian vulnerable persons resettlement scheme (VPRS).

Barrie Grunewald, the leader of St Helens council, told the Guardian that the family had moved into a new home in the town on Thursday having been put up in a hotel since the attack.

A spokeswoman for Refugee Action, the charity that has been supporting the family since they arrived in the UK, said on Thursday they were “really overwhelmed and thankful for the support” after being inundated by well-wishers when news of the attack emerged on Wednesday.

She added that they were “a little bit anxious about all the attention it’s been receiving” but that they were being helped by Refugee Action support workers and housing officers from St Helens council.

Grunewald said he was “sickened to hear of the disgusting attack on a Syrian family who have come to St Helens seeking protection after fleeing conflict in their home country”.

He said he was encouraged by news that the local community had rallied round to help the family and make donations, as well as by the dozens of “heartfelt” comments on social media.

Grunewald added: “St Helens is a great place to come and live. These people are despicable and must be found. I’m so sorry what [the family] have experienced. It’s not typical of St Helens residents and I’m sure they will come together to stamp hate out. If anyone has information please come forward.”

A council official said it was too early to say whether the family would move back to the home that was badly damaged in the fire, but that their wishes would be “paramount in any decision we make”.

St Helens council committed to receiving 60 refugees as part of the Syrian VPRS, which will see 20,000 refugees brought to the UK from camps in Turkey, Lebanon, Iraq, Egypt and Jordan by 2020.

Police are urging anyone with any information about the attack to call 101, quoting incident number 181 of 12 November, or to call Crimestoppers on 0800 555 111.