Samantha Hudson, 27, remained in Scarborough Hospital following a blaze that killed her children, Maddie Hudson, three, Anthony Hudson, five, and nine-year-old William Beale.
The tragedy at the family home in Clarence Avenue, Bridlington, sent the community into mourning and people are praying for Ms Hudson's recovery.
Mayor of Bridlington, Coun Shelagh Finlay, said the whole town was ready to offer support.
"My thoughts are with her and hopefully she'll pull through," she said.
"The community will rally round her when she gets out of hospital.
The Rev Chris McCarthy, vicar of Emmanuel Church in Cardigan Road, said people had lit candles in the church, prayed for Ms Hudson and left money for her.
He said: "It's a big shock for people and one of the main responses we are getting is a lot of young mothers and fathers bringing their children in, lighting candles, and saying they realise it could happen to anybody.
"The sentiment they are sharing with us is it makes us want to cherish our children more and love them more because you never know, and there's an outpouring of great sympathy for the mother.
Police and fire investigators have launched an inquiry to try to establish the cause of the fire, although initial findings suggest it had not been started deliberately.
The fire is believed to have started in the living room while the family were upstairs.
Neighbours raised the alarm after hearing a "bang" and seeing smoke and flames coming from the terrace house.
East Riding councillor Margaret Chadwick, who represents Bridlington South, said: "It's devastating. I just feel so sorry for the mother.