Donations on the 30-year-old's JustGiving page have risen to over £500,000, with her family urging people to keep on giving.
In a statement, the 30-year-old's family said :
Claire would be so happy and overwhelmed with the incredible support that has been offered by thousands of people from all over the world. Her family appreciate the kind messages posted online very much.
Words cannot explain what an incredible, inspirational, beautiful and driven person she was. She was loved by so many and is dearly missed by all of us. For Claire and the Samaritans, please keep the donations coming.
Don't stop giving, just like her. It's what she would have wanted.
Martha Fairlie reports on the legacy of Claire Squires:
The hairdresser from Leicestershire, collapsed in Birdcage Walk, near St James's Park, close to the end of the 26.2 mile course. Tests to establish why she died are expected to take place in the coming days.
Ms Squires has been called an "inspiration" by her close friend Nicola Short. The pair climbed Mount Kilimanjaro for the RAF Association last year, raising £1,500.
Claire is an inspiration to us all. She brought laughter and love to everyone's life. She will be sorely missed by all.
– Nicola Short
Our thoughts and prayers are with her family and friends at this time.
Ms Squires was running the marathon for the Samaritans because her mother has volunteered with the charity for more than 20 years.
She was also motivated to run for them due to the death of her brother from an overdose, the Daily Telegraph report.
Samaritans' Rachel Kirby-Rider told ITV News that they were "devastated" on hearing about her death, and expressed their condolences to her family.
Victoria Hauser, who had known Ms Squires for 15 years, called her "the most amazing person in the world", in an interview with 5 News.
Tributes have also poured in from people on the social media website Twitter.
Big up to everyone who is sponsoring Claire Squires. This brave young woman died trying to help others, so it's the least we can do.
RIP claire squires. Your tragic death has touched the hearts of many and the money raised in your name will help many more #clairesquires
The London Marathon organisers sent their "condolences" in a statement on their website.
The organisers of the Virgin London Marathon would like to express their sincere condolences to the family and friends of the deceased.
We would like to emphasise that our immediate concern is for the family of the deceased. Our thoughts and deepest sympathies are with them at this difficult time.