Mr Leonard voiced his disappointment at the departure of seven MSPs to form a new independent group but insisted it is "time to come together for the future, not divide."
It came as former party leader Kezia Dugdale said Labour must be a "broad church."
He said: "I am of course disappointed that these MPs have decided to leave the Labour party but today’s events will not deter us from our mission of working to achieve real and lasting change here in Scotland, and as part of the wider effort to change the UK.
"Today’s events will simply mean that we will all redouble our efforts to achieve a better and more equal society based on those lasting values.
"The manifesto all Labour MPs stood on in the 2017 general election was and remains a unifying vision. It saw the party make advances, including starting to win back seats in Scotland.
"When young people are fighting for action on climate change, it is time to come together for the future, not divide. The Tory party’s failed solutions represent a dead end. We must do nothing to let them off the hook."
Ms Dugdale had a strained relationship with Mr Corbyn during his time as leader and expressed sympathy for the departing MPs.
She said: "We've got to warn against any idea that the leadership show say Good Riddance to them.
"I think it's a very sad day.
"I want to see a Labour party that's a broad church."