The Competitive Enterprise Institute said that Trump has issued 58 percent fewer major and costly regulations than former President Obama and slashed the Federal Register, the government's rule book, by 32 percent.

And American Action Forumsaid that the Trump administration has saved $560 million by cutting regulations and meeting its promise to eliminate two old rules for every new one.

"As the Trump Administration transitions into the new fiscal year and next phase of Executive Order 13,771, it can reasonably claim net regulatory savings of roughly $560 million under the EO's first phase. There have been some new regulatory costs, but activity on that front remains at a historically low level," said American Action's Dan Goldbeck.

CEI Vice President Clyde Wayne Crews added, "It took a few years for Ronald Reagan to achieve his ultimate, one-third reduction in Federal Register pages following Jimmy Carter's then-record Federal Register. So by this metric, Trump is moving much faster."

Both reports looked at the regulation tally at the end of the fiscal year. The Trump administration postponed its plans for a "cut the red tape" day on Monday after the Las Vegas shootings.