"It is time to take climate action to the next level," Ban told a gathering in Washington that included the mayors of New York and Paris, environmental campaigner Al Gore, business leaders and members of the US Congress.
"We need to accelerate the speed, scope and scale of our response, locally and globally."
The meeting, dubbed Climate Action 2016, came two weeks after 175 countries signed the Paris climate deal at the United Nations, raising hopes that the landmark deal will be quickly ratified.
The Paris agreement will come into force when 55 countries responsible for 55 percent of the world's greenhouse gases have ratified it.
"We cannot afford to lose momentum because with each passing day the climate challenge grows," said World Bank president Jim Yong Kim.
"It seems that every time we look it's worse than we thought," he added, citing record hot temperatures that have now "become the new norm."
Economic growth is already being hit, with some regions seeing a 6 percent drop because of water scarcity alone, said Jim.
Agreed by 195 nations, the Paris deal sets the goal of limiting global warming to "well below" 3.6 degrees Fahrenheit (two Celsius) above pre-industrial levels, by moving to clean energy.
French Environment Minister Segolene Royal sounded upbeat, saying there was a new awareness from many countries that were not fully committed to climate change.
Royal told AFP she wants the Paris agreement to enter into force before the end of this year.
China and the United States have said they will ratify the Paris deal this year and are pushing for others to follow suit so that the agreement becomes operational, possibly as early as late 2016 or in 2017.
Ban said he is convening a similar meeting to the Washington gathering in Beijing in September on the sidelines of the G20 summit to keep climate change high on the world agenda.