Robert K. Hur, the special counsel investigating President Biden’s handling of classified documents while serving as vice president, has interviewed many of Mr. Biden’s closest aides and advisers in a quiet inquiry that over the last nine months has reached into the upper levels of the White House and the cabinet, people familiar with the case said.

Those who have been questioned about how government documents came to be stored in a think tank office set up for Mr. Biden after his vice presidency and in his Delaware home include officials who worked with him both at the tail end of the Obama administration and now.

Among them are Steve Ricchetti, a top White House aide, and Jake Sullivan, the national security adviser, the people familiar with the case said.

Prosecutors have also spoken to Secretary of State Antony J. Blinken, who has been a key Biden foreign policy adviser for decades; Ron Klain, who served as White House chief of staff until earlier this year, and Michael R. Carpenter, the former managing director of the Penn Biden Center, who is currently ambassador to the Organization for Security and Cooperation in Europe. Mr. Blinken’s interview was previously reported by ABC News.

The investigation, overshadowed by more dramatic developments in the special counsel inquiries into former President Donald J. Trump and Hunter Biden, is primarily focused on determining the chain of custody for the documents with classified markings found in the offices of the president’s Washington think tank and at his house in Delaware, the people familiar with the case said.

Mr. Hur’s team has also scrutinized whether longtime Biden aides, and the president himself, adhered to security protocols in handling and packing up official documents and private notes from his vice presidency, they said.

One of the thorniest unresolved issues is whether Mr. Biden will submit to an interview, typically the final stage of an investigation. He could also answer written questions or interact with Mr. Hur’s team through his team of White House and personal lawyers.

A spokesman for Mr. Hur did not comment. A White House spokesman also declined to comment.

Mr. Ricchetti, Mr. Klain and Mr. Blinken have been key advisers to Mr. Biden for over a decade. Mr. Ricchetti, a former lobbyist and adviser to President Bill Clinton and Senator Hillary Clinton, essentially took control of Mr. Biden’s post-vice presidential life. He set up a network of nonprofits and academic institutions that would serve as Mr. Biden’s base of operations, negotiated the former vice president’s lucrative book deal and helped to set up the initial structure of the 2020 campaign.

Mr. Hur’s investigation does not appear to be comparable in scope or seriousness to Mr. Trump’s retention of classified materials at his Mar-a-Lago resort in Florida, which led to his indictment on charges of mishandling national security documents and conspiring with two of his employees to obstruct government efforts to retrieve them.

Mr. Biden’s lawyers immediately notified the National Archives upon discovering the classified documents in late 2022 and have since cooperated with the Justice Department. Mr. Trump, by contrast, put off requests from the archives, initially turned over only a portion of what he had taken, failed to fully respond to a subpoena to return the rest and ultimately was subjected to a search of his home and office by F.B.I. agents with a search warrant.

But the investigation into Mr. Biden, even if it ends without criminal charges, presents political challenges for an incumbent president heading into an election year with low approval numbers.

Mr. Trump has misleadingly portrayed Mr. Biden’s handling of sensitive government documents as equivalent to or worse than his own. Mr. Trump would almost certainly try to spin a decision by Mr. Hur not to prosecute his opponent as proof of a “two-tiered’ system of justice rigged to favor Democrats, according to a person close to the former president.

With the exception of President Barack Obama, every occupant of the Oval Office since Watergate has confronted a special prosecutor scrutinizing him or members of his staff, sometimes for relatively narrow matters but at other times for issues that have mushroomed into at least the threat of impeachment.

In January, Attorney General Merrick B. Garland appointed Mr. Hur, a veteran prosecutor who had worked in the Trump administration, to examine “the possible unauthorized removal and retention of classified documents or other records discovered” at Mr. Biden’s think tank in Washington and at his residences.

Mr. Trump tapped Mr. Hur in late 2017 to run the U.S. attorney’s office in Maryland, where he earned bipartisan praise for his handling of violent crime and public corruption cases. But it was his previous, 11-month stint as the top aide to the deputy attorney general, Rod Rosenstein — as Mr. Rosenstein oversaw the appointment of a special counsel, Robert S. Mueller III, to investigate Mr. Trump’s dealings with Russia — that provided him with experience operating in a hyper-political environment.

Mr. Hur helped run the day-to-day operations of the department at a time of major tumult. From mid-2017 to late 2018, Mr. Rosenstein was under relentless political pressure, including the threat of being fired by Mr. Trump over the appointment of Mr. Mueller, which the president considered a personal betrayal.