President Donald Trump's tweet before the jobs report a week ago has prompted demands for an investigation on whether it allowed market manipulation.

A group of Democratic senators released a letter Friday demanding that various authorities look into the propriety of Trump's release and whether "politicizes economic data and increases the possibility that this inside information could be used for unlawful advantage in the market."

"President Trump recklessly violated federal rules and years of precedent by telegraphing financial data that has the power to move our markets," Senator Elizabeth Warren (D-Massachusetts) said in a statement. "The Trump Administration is swarming with people who have secret financial holdings and conflicts of interest a mile long."

The controversy centered on a tweet Trump sent about an hour before the release of the May jobs report June 1.

"Looking forward to seeing the employment numbers at 8:30 this morning," the president said, though he reportedly already had seen the numbers Thursday evening.

While market reaction was fairly muted, stock futures briefly gained and gold prices and government bond yields moved higher.

Presidents typically have the opportunity to see the jobs numbers the night before the Bureau of Labor Statistics releases them to the public. The White House confirmed that Trump did view the report Thursday evening.

The senators said Trump's tweet sent a clear hint to the market that the report would be better than expected. Indeed, nonfarm payrolls added 223,000 for the month, ahead of Wall Street estimates of 188,000.

They demanded that the Bureau of Labor Statistics, Securities and Exchange Commission, Commodities Futures Trading Commission, and the White House Council of Economic Advisers look into the matter.

"Trump was reckless and irresponsible enough to disclose this information ahead of time, stacking the deck in favor of hedge funds and high-speed traders," Sen Ron Wyden of Oregon said. "We must determine the extent of the president's leaking, its impact on the financial markets and whether Trump's friends benefitted from it."

CNBC has reached out to the individual entities to which the letter is addressed. A CFTC official declined comment. A Labor Department spokesman did not address the letter directly, but noted that "no information or data estimates were released before the official release time."