Steven Ford posted the message six weeks on from his children's tragic death – adding it was the first time he had a full nights sleep.
Jake and Chloe, both aged 23 months, were found dead at their home in Margate, Kent in the early hours of December 27.
Mr Ford, who lives in Ashford, Kent, said on Twitter: "Exactly six weeks on from the worst day of my life, I've actually managed to get a full night sleep. Progress! #strongerthanyesterday."
Jake and Chloe’s mum Samantha Ford, 37, from Margate, has been charged with their murder – the case was briefly heard at Maidstone Crown Court last month.
The grieving dad, who recently marked the day they would have turned two years old, also replied to one friend offering support that he was "sleeping with the light on".
The dad has been regularly posting poignant tributes to the toddlers on social media since their tragic deaths.
Last week he issued poems dedicated to his children through Kent Police.
Mr Ford has also launched a Just Giving page to sponsor him for a white collar boxing event.
So far more than £2,000 has been raised – smashing an initial target of £500.
Exactly six weeks on from the worst day of my life, I've actually managed to get a full night sleep. Progress! #strongerthanyesterday.
On the page, he said: "Thanks for taking the time to visit my just giving page.
"My children were everything to me. They were my world. I've decided to take part in this fund raising event to show that it is possible to live life after death.
"I made a promise to Jake and Chloe that I'll be the best man that I can be. It starts today.
"Jake and Chloe forever xx."
Ford, 37, had initially been expected to attend to enter pleas to two offences of murder but those proceedings have now been adjourned due to delays in producing scientific and psychiatric reports.
Jake and Chloe's bodies were discovered in their beds by police in the early hours of December 27.
The toddlers were found by cops after Ford allegedly crashed her car into the back of a lorry on the A299 near seaside town Whitstable, Kent.
She survived with minor injuries and officers took her the 15 miles back to her Margate home where they found Jake and Chloe.
Paramedics rushed the children to hospital where they were pronounced dead shortly after arriving.
At inquest hearing on January 8 was told a post-mortem examination had not established the precise cause of death.
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