WASHINGTON — The Federal Reserve’s inspector general concluded Thursday that financial trades made several years ago by Chairman Jerome Powell and the former vice chairman, Richard Clarida, did not violate any laws or ethics rules.

“We did not find evidence to substantiate the allegations” that Messrs. Powell or Clarida “violated laws, rules, regulations, or policies related to trading activities as investigated by our office,” Inspector General Mark Bialek said in a July 11 letter to Mr. Powell, released Thursday.

At the same time, the letter said the investigation of the presidents of two regional Federal Reserve banks who stepped down after their trading activities came to light remains ongoing.

The investigation stemmed from disclosures last year that several Fed officials had bought and sold stocks, real estate investment funds and other securities during periods of sharp market turmoil in the spring of 2020 after the pandemic had erupted. The trades occurred during a time when the senior officials were privy to discussions about Fed decisions that would likely affect those markets.

The transactions created the appearance of impropriety, Mr. Powell has acknowledged. The Fed also adopted sweeping new rules that sharply limit officials’ trading activities.

The inspector general’s report said that Mr. Clarida acknowledged last fall that he had omitted four trades from financial disclosure forms. He filed amended forms with the federal government’s Office of Government Ethics, which concluded that the trades, in several index-style investment funds, did not constitute conflicts of interest.

“I am gratified by the conclusions,” Mr. Clarida said in a statement. The investigation “determined conclusively that I did not violate any statutes, rules, regulations, or standards.”

Mr. Clarida resigned early this year and was succeeded by Vice Chairwoman Lael Brainard.

Still, Mr. Clarida came under criticism from ethics groups in Washington in January for the amendments he had made to his trading disclosures. Those changes, along with his original report, showed that he sold shares of a stock fund on February 24 and bought shares in the same fund February 27. 

A day later, Powell issued a statement that said COVID posed a risk to the economy and said the Fed “will use our tools” to support growth — a policy move that could have affected the investments the officials had made.

A spokesman for Mr. Clarida, Salvatore Antonio “Tony” Fratto, said the sale was intended as a pre-planned rebalancing of his portfolio. Yet after the initial sale, Clarida decided to buy the shares back instead of shifting the funds into other investments.

Mr. Fratto said the fund Clarida invested in — an iShares exchange-traded fund managed by asset manager BlackRock — was approved by the Fed and would be acceptable even under its current, more stringent rules.

The inspector general’s report did not specifically address the issue of the timing of Mr. Clarida’s trades. But it said that overall, they did not violate any laws, regulations or policies.

The report found that a Powell family trust made five trades in December 2019 on the date of a policymaking meeting, when senior officials aren’t supposed to trade. But the inspector general concluded that the trades were conducted by a financial adviser and that neither Mr. Powell nor his wife were aware of them.

The chief executive of watchdog group Better Markets, Dennis Kelleher, criticized the report for not addressing whether the trades violated several Fed policies that require senior officials to avoid creating “even an appearance” of conflict between their financial interests and the public interest.

“The report is very narrow, omits key information and is not credible,” Mr. Kelleher said.

Both Messrs. Powell and Clarida worked in the financial sector before joining the Fed and have each reported net wealth in the tens of millions of dollars. Mr. Powell worked at the Carlyle Group, a private equity firm, Mr. Clarida for Pacific Investment Management Company.

Last year, the presidents of two of the Federal Reserve’s regional banks — Robert Kaplan of the Dallas Fed and Eric Rosengren of the Boston Fed — resigned after the disclosures came to light.

In October, the Fed announced wide-ranging changes to its trading rules. Under its new policies, Fed officials — including senior staff — are barred from investing in stocks, bonds, cryptocurrencies or commodities and cannot hold industry-specific mutual funds. They are also required to provide 45 days’ advance notice before buying or selling securities and to publicly disclose all their transactions within 30 days.

But on Wednesday, Senator Brown, a Democrat from Ohio and chairman of the Senate Banking Committee, and several colleagues, urged the Fed to adopt tougher rules, including more specific consequences for violations.

The Fed’s new policy “fails to set forth any standards for disciplinary action, financial penalties, or other meaningful consequences for violations,” Mr. Brown said in a letter.