In January, President Trump signed an executive order that put in place stringent ethics rules for his political appointees like Mr. Bannon. Under the policy, Mr. Bannon would be barred from contacting Breitbart employees for two years to discuss issues that were under his purview while he was an executive there.

But Mr. Bannon continued those communications, including with Breitbart editors, after beginning his job as Mr. Trump’s chief strategist on Jan. 20, according to a complaint by Citizens for Responsibility and Ethics in Washington, a liberal group.

Some critics have raised concerns about Mr. Bannon’s ties to Breitbart, which he helped build into a formidable conservative media force before leaving last August to join Mr. Trump’s presidential campaign. The complaint alleged that Mr. Bannon’s discussions with the media organization — in his official role as chief strategist — “resulted in Breitbart receiving preferential access to senior members of the Trump administration.”

The complaint was filed with the White House Counsel’s Office, which has the ability to investigate and issue a punishment, if it deems one necessary. It has not commented publicly on the complaint.

But in another recent case, after complaints from several groups, the counsel’s office disclosed that it found that another top adviser, Kellyanne Conway, had acted “inadvertently” by promoting the brand of Ivanka Trump, Mr. Trump’s daughter, during an interview on Fox News in February. It said Ms. Conway was “highly unlikely” to err again.

The Office of Government Ethics, which is the chief ethics monitor for the federal government, does not have the authority to investigate complaints. It did issue an opinion during the Obama administration maintaining that retroactive ethics waivers were not allowed, and noted several instances where they appeared to have been granted after the fact.

“Waivers and authorizations must be issued prospectively in order to be valid,” Don Fox, the general counsel of the ethics office, wrote in April 2010. He wrote that the process of evaluating waivers was one of the more significant duties of ethics officials. “Both the individual employee’s interests and those of the government are best served when this process is carried out in a careful and consistent manner.”