President Trump did try to have the Secret Service take him to the Capitol on the afternoon of Jan. 6, 2021, but agents with him in the limousine rebutted a claim that when he was denied he tried to grab the wheel and force the vehicle, according to a new inspector general’s report.

The account contradicts the testimony of former White House aide Cassidy Hutchison, who assisted Democrats’ Jan. 6 investigation with her claim that an “irate” president grabbed the steering wheel and demanded to join the pro-Trump protesters.

Investigators said there was never a plan for Mr. Trump to go to the Capitol. Agents had discouraged the idea early on.

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Then on Jan. 6, after he addressed a rally at the Ellipse, Mr. Trump asked if he could go but was told the roads made it impossible.

The inspector general spoke with agents who were in the car and while the driver said Mr. Trump was angry at not being allowed to go, another agent said he didn’t recall that being the case. And several agents denied the wheel-grabbing claim.

“We asked [redacted] agents whether the President reached for the steering wheel of the limousine or lunged toward the detail lead when his request to go to the Capitol was denied, and [redacted] witnesses said those actions did not occur,” the audit said.

The drive happened after Mr. Trump left the Ellipse, where he’d ended his speech to supporters with an exhortation to march to the Capitol, where lawmakers were conducting the Electoral College vote count that confirmed his defeat in the 2020 election.

Mr. Trump left the rally at 1:16 p.m. and was back at the White House by 1:19.

By that time, Capitol Police were already confronting rioters. The Capitol would be breached after 2 p.m.

Ms. Hutchison was one of the Democrats’ star witnesses in their Jan. 6 investigation with her ability to deliver an inside account. She said her story about the steering wheel came from a deputy chief of staff. The inspector general said that the official denied the account.

The inspector general confirmed that there were some “near encounters” with rioters and then-Vice President Mike Pence.

Secret Service agents had moved Mr. Pence from the Senate chamber at 2:12. Protesters reached the area outside the Senate chamber three minutes later. They were diverted by a Capitol Police officer. Had that officer not led them away, the audit said, the rioters could have found the vice president and his family.

The heavily redacted report also details the Secret Service’s efforts to remove then-Vice President-elect Kamala Harris from the headquarters of the Democratic National Committee after a pipe bomb was found just outside the building.

But the report says Ms. Harris’s motorcade passed within 20 feet of the pipe bomb earlier before it was discovered.

The inspector general said the Secret Service had explosives-detection dogs on site but it didn’t have clear guidance about where to sweep. There also was no explosive ordinance disposal team on site.

In an official response to the audit Kimberly Cheatle, who was ousted as Secret Service director last month after Mr. Trump was nearly assassinated, said the inspector general’s investigation was worrying.

She said the inquiry was too broad and covered “highly sensitive” communications from top leaders that she felt were beyond the scope of the events of Jan. 6. She hinted that Homeland Security Secretary Alejandro Mayorkas, who oversees the Secret Service, could have been asked to shut down the audit.

Republicans have been demanding release of the report, saying Mr. Mayorkas was keeping it from the public. GOP lawmakers went public with their demands last month.

The report was released after business hours Friday evening.

Republicans said the report showed a striking effort to undermine the independent inspector general, including Ms. Cheatle’s resistance to turning over communications and the deletion of text messages that Congress and the inspector general had asked to be preserved.

Ms. Cheatle said they were deleted as part of a pre-scheduled data “migration” but the House Administration Committee said that should have been put on hold once Congress and the inspector general sought the information.