The United States is making great strides toward the goals pledged in the Paris agreement to combat climate change with virtually no help from the federal government, billionaire Mike Bloomberg told CNBC on Tuesday.

The former New York mayor and co-author of the new book "Climate of Hope" said on "Squawk Alley" he hopes President Donald Trump will change his mind about pulling out of the Paris agreement, which was signed last year.

"I hope Donald Trump will listen to some of his staff and become convinced that he should be very pro-environment," he said at BTIG's 15th annual charity day in New York. "I hope he changes his mind and he listens to his daughter, who's supposedly a big advocate of staying the course."

Ivanka Trump and her husband, Jared Kushner, also an advisor to her father, side with Secretary of State Rex Tillerson, formerly CEO of ExxonMobil, to remain in the climate deal. Trump advisor Steve Bannon and EPA Administrator Scott Pruitt want the U.S. to pull out.

The Paris accord, with nearly 200 countries on board, calls for cutting carbon dioxide and other emissions from the burning of fossil fuels, believed to be the cause of climate change.

As part of the deal, the U.S. under Trump's predecessor President Barack Obama committed to reducing its emissions by between 26 percent and 28 percent below 2005 levels by 2025.

"Even if [Trump] doesn't change his mind, it's the private sector that has reduced greenhouse gases. We are two-thirds of the way already towards the targets for 2025 without any help from the federal government," Bloomberg said. "So we're going to make this regardless."

— Reuters contributed to this report.