Senate Armed Services Committee Chairman John McCain (R-Ariz.) speaks with members of the media inside the U.S. Capitol. (Mark Wilson/Getty Images)

Senators who attended a closed-door Pentagon briefing Thursday on the militant ambush in Niger that left four U.S. soldiers dead commended the military for progress in investigating the Oct. 4 attack. But many complained that they were left with more questions than answers.

Senate Armed Services Committee Chairman John McCain (R-Ariz.) said he was willing to wait the 30 days he said the military was likely to need to complete its inquiry into how a train and assist mission in West Africa turned into a deadly confrontation with armed extremists.

McCain declined to give the Pentagon an indefinite timeline to conduct its investigation free from congressional scrutiny, although such inquiries typically take months. While Thursday's briefing "is what we've been asking for," he said, senators still "expect more."

As lawmakers demanded additional information, the Pentagon's top general said he was frustrated with the "drip, drip, drip" of details about the attack being reported in the media. Speaking aboard a flight to South Korea, Marine Gen. Joseph F. Dunford Jr., chairman of the Joint Chiefs of Staff, said that "everyone is doing their job" in examining the incident.

"It's the world as it is," Dunford said of ongoing leaks and speculation about the incident. "I'm not making a judgment here. But I would just tell you, my preference would be to get a single document" that outlines the final results of the investigation.

Soldiers carry the transfer case containing the body of Staff Sgt. Dustin M. Wright, one of the four Americans killed in Niger on Oct. 4. (Pfc. Lane Hiser/AP)

At a Pentagon briefing for reporters Thursday, Lt. Gen. Kenneth F. McKenzie Jr., director of the Joint Staff, declined to discuss news reports that the ambushed soldiers were part of a larger mission to track down a suspected militant leader.

"There are other teams that operate in Niger . . . [including] one that had something to do with this operation," McKenzie said. "But I'm not able to give you more specific details" until the investigation concludes. "We just want to make sure we get the timeline right and understand the totality of it before we bring it forward."

The ambush, in southwestern Niger, caught a team of 12 soldiers with the 3rd Special Forces Group and 30 Nigerien soldiers partnered with them after they visited a village two hours south of their base in the capital of Niamey. McKenzie repeated earlier Pentagon statements that the visit was similar to dozens carried out previously and that any hostile contact was considered "unlikely." Five Nigerien soldiers were also killed.

The bodies of three of the dead U.S. soldiers were recovered the same day. The body of Army Sgt. La David T. Johnson, a conventional U.S. soldier who worked as a mechanic attached to the team, was not found for two days, prompting senior U.S. officials to deploy elite U.S. commandos with Joint Special Operations Command to search for him.

Several senators said after the Thursday briefing that military officials were unable to tell them why it took so long to find Johnson. On other matters, however — including how the ambush happened in the first place — lawmakers came away with differing impressions.

Sen. Ted Cruz (R-Tex.) said he was confident "there were not significant steps that could have been taken to prevent this assault." But McCain argued that "whenever there's a failure, it could be prevented," saying that the soldiers' deaths were caused by both bad luck and bad strategy.

McCain and others have complained in recent weeks that the Pentagon has kept Congress in the dark about details of ongoing operations, in particular the military's expanding mandate in Africa. Last Friday, McCain and Sen. Lindsey O. Graham (R-S.C.) said Defense Secretary Jim Mattis had told them that the military, under less restrictive counterterrorism rules that President Trump has put in place, would increase its focus on Africa as the Islamic State loses its strongholds in Iraq and Syria.

That has led some senators to look more favorably on passage of a new Authorization for the Use of Military Force (AUMF), more reflective of current threats, replacing one passed immediately after the September 2001 al-Qaeda attacks on the United States. The measure has been stalled for years in Congress over deep disagreement about what it should say.

In the days since the Niger attack, it has been difficult to find a senator still willing to say that a new authorization is not desirable, although there is still little consensus on its terms.

Sen. Tim Kaine (D-Va.), who has co-authored a proposed new AUMF that will be the focus of a hearing with Mattis and Secretary of State Rex Tillerson on Monday, warned after the briefing that the military was not being forthright enough with the U.S. public about how as many as 6,000 troops in Africa were being used.

"I think the extent of the ­operations, the number of countries, would be surprising," Kaine said.

In programs begun under the Obama administration, and in some cases before, the U.S. military operates noncombat training missions in many African countries, as well as a major base in Djibouti and smaller facilities elsewhere. Although the number of troops has steadily increased in recent years, lethal strikes against suspected terrorists are allowed only in Libya and Somalia.

Dan Lamothe in Seoul and Karen DeYoung in Washington contributed to this report.