Mr Trump had reportedly been discussing the idea of an efficiency commission with aides for weeks but Thursday was the first time he had publicly endorsed the idea.
It was also the first time Mr Trump said that Mr Musk had agreed to head the body. He did not detail precisely how such a commission would operate, besides saying it would develop a plan to eliminate “fraud and improper payments” within six months of being formed.
The US government already has the Government Accountability Office (GAO), a federal watchdog agency tasked with investigating federal spending and performance.
Mr Musk, the world’s richest man, has a reputation for presiding over hard-charging cultures at his businesses, demanding high performance.
After buying formerly Twitter with outside investors for $44bn (£33.4bn) two years ago, he sacked 6,000 staff – around 80pc of the workforce. Mr Musk said Twitter needed to become more “hardcore” to survive.
At the time, critics claimed the job cuts would put the social media platform at risk of technology meltdown. However, the platform, since renamed X, has continued to function.
Mr Trump’s promise to hire Mr Musk, one of his most high-profile supporters, was part of a broader pitch to business leaders including Jamie Dimon, JP Morgan chief, and Stephen Schwarzman, managing director of Blackstone, at the New York Economic Club event.
The Republican nominee also vowed to cut corporation tax from 21pc to 15pc. He told the audience: “I am promising low taxes, low regulations, low energy costs, low interest rates, secure borders, low, low, low crime.”
Mr Trump’s proposal for a new efficiency watchdog immediately drew criticism from trade unions. Everett Kelley, head of the American Federation of Government Employees, accused Mr Trump and Mr Musk of wanting to gut the non-partisan civil service and replace workers with allies.
“There’s nothing efficient about that,” he said.