Riley, 36, wrote: "A sombre International Women’s Day today. Big responsibility raising girls.
"Every time we pack up what feels like half our belongings take with us to Manchester to look after two little ones for 3 days filming, I’m thinking of the women who’ve had to pack up their lives into their car, or bags, say goodbye to their men, and leave everything for who knows how long. We’re so lucky to be living in peace with our family in tact.
"Thinking of the millions who aren’t and trying to do the small things we can to help."
The Countdown letters board paid tribute to four-month-old Noa, who was born on 5 November last year.
She followed two-year-old Maven who was bon in December 2019.
Kovalev, 42, and Riley met during the 2013 series of Strictly Come Dancing, where they were partnered together.
The couple married in Las Vegas in June 2019 a month after announcing they were expecting their first child together.
Kovalev moved from his home nation of Russia to the USA in 2001 to pursue his dance career and then relocated to the UK a decade later to take part in Strictly.
He recently shared on Instagram: "Our passport may say one thing but our hearts are with our family, friends and everyone still in Ukraine that are fighting for freedom and lives.
"It only feels right that our show Rise Up with the Arts, along with 3 charities that we are already supporting, will now focus on donating funds raised to the Save The Children charity that helps children and young people affected by this terrible conflict.
"They say it takes a village to raise a child but this time it will take the whole world to make the change happen and end this madness. Let's make art not war."
Russian President Vladimir Putin began the invasion of Ukraine on 24 February, prompting thousands of Ukrainians to attempt to flee the country.
Watch: Countdown letters spell unfortunate phrase on Rachel Riley's 3000th episode