Coun Judith Blake told the Yorkshire Evening Post that the speed with which the city’s rivers had risen through Saturday had been “really, really terrifying”.
She went on: “I want to thank everybody who has been working so hard in such awful circumstances.
“The council, the Environment Agency and, of course, the health workers who have been doing extraordinary things to reach vulnerable people.”
Coun Blake said she would be visiting the city centre today as efforts continue to assess the scale of the damage.
She also said she would be speaking to the Government about what support it could offer the clean-up operation.
The council’s chief executive, Tom Riordan, took to Twitter to send “huge thanks” to all those involved with the response to the crisis, including public service teams, businesses, volunteers and emergency services.
Meanwhile, Leeds Central MP Hilary Benn has called for more investment in flood defences in the wake of the weekend’s chaos.
Mr Benn, Labour’s former environment secretary, said: “This is the worst we have ever seen. These are the highest levels that have been experienced in the centre of the city.”
He added: “The need for improved flood defence is increasing really fast because the climate is changing.”
Mr Benn also said: “Individuals need to think about what they can do if it’s possible to protect their own properties, but what this reminds us all is that nature is more powerful than us as human beings.”
The debate about climate change was over, he claimed, because he said there was “no doubt” the world’s climate is now different.
Mr Benn said countries needed to prioritise reducing emissions by honouring promises made at this month’s climate change negotiations in Paris.
He added: “The second thing is we’ve got to adapt to the changing climate, and improving our flood defences is one of the urgent ways we need to do that.”