Two Federal Reserve officials embroiled in controversy for trading securities that could have benefited from the central bank’s 2020 intervention in financial markets announced on Monday that they would leave their positions.

Robert S. Kaplan, who heads the Federal Reserve Bank of Dallas, will retire on Oct. 8, according to a statement released Monday afternoon. Mr. Kaplan’s statement acknowledged the controversy as the reason for his departure. Eric S. Rosengren, the president of the Boston Fed, will retire this Thursday, accelerating his planned retirement by nine months. Mr. Rosengren cited health reasons for his early departure.

The resignations followed the Fed’s announcement this month that Chair Jerome H. Powell had ordered a review of the central bank’s ethics rules in light of the concern surrounding the trades. When asked about his confidence in Mr. Kaplan and Mr. Rosengren during a news conference last week, Mr. Powell expressed displeasure with what had happened.

“No one on the F.O.M.C. is happy to be in this situation, to be having these questions raised,” Mr. Powell said, referring to the policy-setting Federal Open Market Committee. He added, “This is an important moment for the Fed and I’m determined that we will rise to the moment.”

Mr. Kaplan noted in his statement that it was his decision to leave the Fed, and that “the recent focus on my financial disclosure risks becoming a distraction” to the central bank’s economic work.

Mr. Kaplan drew scrutiny for buying and selling millions of dollars in individual stocks, among other investments, last year — trading first reported on by The Wall Street Journal on Sept. 7. He has maintained that his trades were consistent with Fed ethics rules.

Mr. Rosengren announced on Monday morning that he was retiring earlier than planned to try to prevent a kidney condition from worsening, in the hopes of staving off dialysis. The Boston Fed president came under criticism because he held stakes in real estate investment trusts, which invest in and sometimes manage properties, and listed purchases and sales in those in 2020. He spent last year warning publicly about risks in the commercial real estate market, and was helping to set Fed policy on mortgage-backed security purchases, which can help the housing market by improving financing conditions.

Both presidents had previously announced that they would convert their financial holdings into broad-based indexes and cash by Sept. 30.

Mr. Powell offered statements of support for both of the retiring officials in the news releases announcing their exit.

But the controversy has pushed him into a delicate position. His own term as Fed chair expires early next year, and the White House is actively considering whether to reappoint him. A scandal at his central bank is sure to draw questions from senators when he testifies this week, and could even hurt his reappointment chances.

As chair, Mr. Powell has also focused on shoring up public support in the central bank and explaining its role. He holds frequent news conferences, aims to speak in simpler language, and championed a series of “Fed Listens” events where top central bank officials meet and hear from community members whom they might not otherwise interact with — from community college students to local food pantry staff.

The 2020 trading disclosures, which are shaping up to be the most headline-grabbing scandal the central bank has faced in years, risk chipping away at the widespread trust he has been working to build.

Responses to Mr. Kaplan and Mr. Rosengren’s trading disclosures have been swift, and scathing. The group Better Markets had been calling for the Fed to fire both presidents if they did not resign. Other progressive groups had called for at least one of them to be ousted, and ethics watchdogs have said that the rules that had enabled their trades needed to be revisited.

After the resignation announcements on Monday, Wall Street promptly began to assess what the departures would mean for monetary policy. Both officials have tended to worry about financial stability, and for that reason were likely to favor removing monetary policy support sooner than some of their colleagues — a stance often referred to as being hawkish.

“Their exit will take out two of the nine more hawkish Fed officials who saw a 2022 rate hike as of the September F.O.M.C. meeting last week and remove important voices on financial stability issues in particular,” Krishna Guha at Evercore ISI wrote in a note to clients shortly after the announcement.

Mr. Rosengren has been president of the Boston Fed since 2007, and his retirement was previously planned for June. The Fed’s 12 regional members rotate in and out of voting seats, and Mr. Rosengren would have had a vote on monetary policy next year. Mr. Kaplan would have voted in 2023.

Kenneth C. Montgomery, the Boston Fed’s first vice president, will serve as interim president at that bank. The Boston Fed’s board members — excluding bank representatives — will need to select a permanent pick for president, subject to approval from the Fed’s Board of Governors in Washington.

A longtime Fed employee who worked in research and bank supervision before becoming president, Mr. Rosengren played a key role in the 2020 crisis response. His regional Fed ran both the money market mutual fund and Main Street lending backstop programs that the Fed rolled out last year.

The Boston Fed noted in the release that Mr. Rosengren hoped that his health condition would improve, and that he would be able to “explore areas of professional interest” in the future.

Mr. Kaplan has been at the head of the Dallas Fed since late 2015, before which he taught at Harvard University and had a long career at Goldman Sachs. Meredith Black, that bank’s first vice president who had planned to retire, will serve as interim president until a successor is named, the Dallas Fed said.