US Senator Kelly Loeffler (L), R-GA, and husband Jeffrey Sprecher, CEO of Intercontinental Exchange and Chairman of the New York Stock Exchange, on January 6, 2019.

The Securities and Exchange Commission on Monday issued a sharp warning against trading on nonpublic information related to the coronavirus — a caution that came days after news of recent stock sales by the CEO of the owner of the New York Stock Exchange and his senator wife sparked widespread criticism and calls for investigations.

The statement from the SEC's co-directors of enforcement about "market integrity" did not refer to those trades by NYSE Chairman Jeff Sprecher and Sen. Kelly Loeffler, R-Ga., or trades by three other senators in the past two months.

Sprecher and Loeffler's trades, involving sales of up to $3 million worth of securities, came in the weeks before stock market indexes dramatically fell in value due to the coronavirus pandemic, and on the heels of a private, all-senators briefing on the virus outbreak from Trump administration health officials that Loeffler attended on Jan. 24.

In addition to Loeffler's move, recently disclosed stock sales by three other senators, Richard Burr (R-NC), James Inhoffe (R-OK) and Diane Feinstein (D-CA) have come under scrutiny and criticism because they occurred after that coronavirus briefing.

Loeffler said last Friday that the trades detailed in Senate disclosure forms were made by third-party financial advisors, without input or the knowledge by either her or Sprecher, who is CEO of the Big Board's holding company, Intercontinental Exchange.

Over the weekend, CBS News, citing public SEC filings, reported that in addition to those trades, Sprecher on Feb. 26 sold $3.5 million in shares of of his company, Intercontinental Exchange, or ICE, at an average price of $93.42 each. ICE shares have since dropped almost 25%.

Other SEC filings cited by CBS show that Sprecher and Loeffler "also sold $15.3 million worth of ICE shares on March 11, at an average price of around $87 per share."

Loeffler is, by far, the richest member of Congress, sharing a net worth of about $500 million.

The SEC directors in their statement noted that, "The 2019 coronavirus disease (COVID-19) has impacted the securities markets in unprecedented ways."

"In these dynamic circumstances, corporate insiders are regularly learning new material nonpublic information that may hold an even greater value than under normal circumstances," the directors, Stephanie Avakian and Steven Pelkin said.

"This may particularly be the case if earnings reports or required SEC disclosure filings are delayed due to COVID-19," the directors said.

The statement said that "given these unique circumstances, a greater number of people may have access to material nonpublic information than in less challenging times."

"Those with such access – including, for example, directors, officers, employees, and consultants and other outside professionals – should be mindful of their obligations to keep this information confidential and to comply with the prohibitions on illegal securities trading," the directors wrote.

"Trading in a company's securities on the basis of inside information may violate the antifraud provisions of the federal securities laws."

The SEC declined to comment when asked if the new statement was spurred by last week's news about recent trading by Sprecher and Loeffler, and whether the SEC is investigating those trades.

Neither Sprecher nor Loeffler, nor the three other senators have been accused of wrongdoing by the SEC or any other regulatory or law enforcement agency.

Financial disclosure forms filed recently by Loeffler reveals that accounts owned by the couple had almost 30 trades in stocks since Jan. 24, the day that she and other senators were briefed about the coronavirus by Trump administration officials. The sales began on the day of that briefing.

Over the next three weeks, Loeffler and Sprecher sold shares worth $1.25 million to $3.1 million, according to disclosure records.

But on Feb. 14, accounts owned by Loeffler and Sprecher bought stock in Citrix, which provides teleworking software, and in Oracle, the technology company.

Many Americans have been working remotely from home as companies closed or reduced staff at their physical offices due to the COVID-19 crisis.

Intercontinental Exchange, which owns other exchanges and clearing houses in addition to the NYSE, said in a statement last week that all of the transactions involving the couple were "in compliance" with company policies.

"Mr. Sprecher and Senator Loeffler have made clear that those transactions were executed by their financial advisors without Mr. Sprecher's or Senator Loeffler's input or direction," the company said.

"Such transactions are in compliance with Intercontinental Exchange, Inc. policies and procedures."

Loeffler, in an interview with CNBC's "The Exchange" last Friday, said "I am very confident that we have followed the letter and spirit of the law."