One year ago, President Trump announced the U.S. would exit the Paris climate agreement. Former New York City mayor and billionaire Michael Bloomberg is working to bypass Mr. Trump's opposition to the agreement, launching a new effort today to help the U.S. achieve the goals adopted by the Obama administration.

The centerpiece is a $70 million American Cities Climate Challenge, a program that will select 20 U.S. cities and help them speed up their efforts to reduce greenhouse gas emissions. The program aims to push the U.S. toward meeting the goal it set in the Paris talks of cutting greenhouse gases by 26 percent, from 2005 levels, by 2025.

Bloomberg, who co-wrote the bestselling book "Climate of Hope" with Carl Pope, acknowledged he jokes about how Mr. Trump's opposition has helped spur more action on climate change and other issues.

"It's easy to raise money for sensible gun regulations and the background checks and for climate change things because he's come out, and I've joked that I want him to do more," Bloomberg said Friday on "CBS This Morning.

But his actual hope, Bloomberg said, is that the president – whom he believes is "getting bad advice" – will change his mind.

"We've watched him. He can change his mind. He changes it frequently. Hopefully he'll come around and do something that makes some sense. Not doing anything about climate change really just makes no sense whatsoever and it jeopardizes all of us," Bloomberg said.

He said children and adults have greater risk of health issues, including asthma attacks and stomach cancer, without clean air or water.

"So if you don't worry about the future, just worry about you and your family today and you'd do the same thing," Bloomberg urged.

Bloomberg said the private sector is key to making progress on the issue of climate change.

"The federal government doesn't have a lot to do with climate change... President Obama did get a law passed. Donald Trump said stop the law. He didn't; it's been tied up in the courts and never put into place. So the federal government's not involved," Bloomberg said. "The state governments, only a little. It's city governments and the private sector. Mostly the private sector."

He also said corporations are under pressure from investors, employees and customers to be more "climate friendly."

Bloomberg said he's worried about what's happening in the world.

"Nobody knows where it's going. Scientists have theories about it, but the direction is horrendous. It was 122.4 degrees in Pakistan two weeks ago. It was over freezing in the North Pole. Seventeen out of the 18 warmest years on record since have been since the year 2001. Something is going on and it just makes no sense to continue in the direction we're going," Bloomberg said.

So he's taking "prophylactic actions now" with a focus on what cities can do.

"Cut back greenhouse gasses, increase the fuel efficiency of cars, things like that. Generate solar and wind power, which is cheaper now than fossil fuel power. It's good economics, it creates jobs and it protects us from what might happen in the future," Bloomberg said.