David C. Weiss, the special counsel investigating Hunter Biden, said on Wednesday that he planned to indict the president’s son on a gun charge before the end of the month — a move prompted by the acrimonious collapse of a plea deal in July.

In a three-page update filed in federal court in Wilmington, Del., Mr. Weiss laid out plans to bring charges related to Mr. Biden’s purchase of a pistol in 2018, when prosecutors say he lied on a federal form by stating that he was not using drugs at the time. Mr. Biden had previously agreed to participate in a two-year diversion program for nonviolent gun offenders as part of the plea deal, which unraveled dramatically at the last minute this summer.

Mr. Biden’s lawyer, Abbe Lowell, signaled in a statement that he would challenge any effort to proceed with a trial, arguing that the original agreement reached over the summer “remains valid and prevents any additional charges from being filed.”

The government’s filing, while expected, adds an additional and volatile element to an already packed calendar of criminal cases coinciding — and colliding — with the 2024 presidential race. It piles on a possible federal trial of President Biden’s son to former President Donald J. Trump’s two federal and two state criminal cases.

The status report by Mr. Weiss was filed at the request of a federal judge. It makes no mention of the status of likely separate charges stemming from the five-year investigation of Mr. Biden’s business dealings, and subsequent failure to pay taxes, conducted by Mr. Weiss, the U.S. attorney in Delaware who was appointed last month as a special counsel after overseeing the investigation. Last month, prosecutors told the court they intended to file the tax charges in either California or Washington, D.C.

Leo Wise, a veteran prosecutor detailed to Mr. Weiss’s team in June, said in the court filing on Wednesday that the Justice Department would seek the return of an indictment on the gun charge before Sept. 29, citing a timetable set by the Speedy Trial Act.

Mr. Biden appeared to be just hours away from resolving his legal troubles this summer through a deal that would have cleared up both the tax and gun investigations. But under questioning by a judge in federal court in Wilmington, prosecutors and defense lawyers were forced to acknowledge that they had very different interpretations of the terms of the agreement, leading to its collapse.

After subsequent negotiations to revive an agreement on the tax and gun charges foundered, Attorney General Merrick B. Garland elevated Mr. Weiss to the status of special counsel, giving him more flexibility in pursuing the tax charges and the freedom to continue investigating other elements of the case.

Under the original deal, Mr. Biden had agreed to plead guilty to two tax misdemeanors and to settle the gun investigation without being charged.

Despite the collapse of the agreement, Mr. Lowell said that his client had been abiding by the terms of the original deal “for the last several weeks” and had been making regular visits to his court-assigned probation officer.

Mr. Lowell suggested that he was continuing to pursue a “fair” deal with Mr. Weiss, not subject to “outside political pressure.”

Mr. Weiss is the third special counsel appointed since Mr. Garland took office in March 2021, joining Jack Smith, who is overseeing the investigations of Mr. Trump, and Robert K. Hur, who is examining President Biden’s retention of sensitive documents from his tenure as vice president.

The gun charge stems from Hunter Biden’s response of “no” on a federal form he filled out as part of the purchase of a handgun when asked whether he was an “unlawful user” of drugs. At the time, Mr. Biden, who had been addicted to crack cocaine, was struggling to remain sober.

Such federal prosecutions are relatively rare, and seldom pursued as stand-alone charges. Officials at the Bureau of Alcohol, Tobacco, Firearms and Explosives responsible for reviewing Mr. Biden’s file were skeptical of bringing charges against him, especially considering that he had sought treatment and had no prior criminal history, according to another person with knowledge of the situation. (The widow of his brother, Beau, later found the gun and threw it in a dumpster.)

Another factor that could complicate the government’s case: Last year’s Supreme Court ruling that gave people a broad right to carry guns outside the home. Mr. Biden’s lawyers have argued that recent lawsuits challenging federal regulations, including the drug use restriction, could render a prosecution of Mr. Biden moot.