The Pentagon leadership suggested to a Senate panel on Tuesday that US ground troops may directly join Iraqi forces in combat against the Islamic State (Isis), despite US president Barack Obama’s repeated public assurances against US ground combat in the latest Middle Eastern war.

A day after US warplanes expanded the war south-west of Baghdad, Army General Martin Dempsey, the chairman of the Joint Chiefs of Staff, told the Senate armed services committee that he could see himself recommending the use of some US military forces now in Iraq to embed within Iraqi and Kurdish units to take territory away from Isis.

“If we reach the point where I believe our advisers should accompany Iraqi troops on attacks against specific [Isis] targets, I will recommend that to the president,” Dempsey said, preferring the term “close combat advising”.

It was the most thorough public acknowledgement yet from Pentagon leaders that the roughly 1,600 US troops Obama has deployed to Iraq since June may in fact be used in a ground combat role, something Obama has directly ruled out, most recently in a televised speech last week.

Dempsey, who has for years warned about the “unintended consequences” of Americanizing the Syrian civil war that gave rise to Isis, said he envisioned “close combat advising” for operations on the order of taking Mosul, Iraq’s second largest city, away from Isis.

He also opened the door to using US “advisers” to call in air strikes from the ground, something Dempsey said they have thus far not done but which the US Central Command leader, General Lloyd Austin, initially thought would be necessary when pushing Isis away from the Mosul Dam last month.

“He shares my view that there will be circumstances when we think that’ll be necessary, but we haven’t encountered one yet,” said Dempsey, himself a veteran of the last Iraq war.

Obama’s prohibition on ground forces in a combat role was less ironclad than the president has publicly stated, Dempsey suggested.

“At this point, his stated policy is we will not have US ground forces in direct combat,” Dempsey said, to include spotting for US air strikes. “But he has told me as well to come back to him on a case-by-case basis.”

Joined by Defense secretary Chuck Hagel, Dempsey said the latest US war in Iraq, and soon in Syria, will last several years and will not resemble the “shock and awe” aerial bombardment that characterized the opening phase of the 2003 US invasion.

Isis’s ultimate defeat will be a “generational” effort, Dempsey said, during which “moderate” Muslims abandon its ideology – raising questions about what the US military’s actual endpoint will be in pursuing the goal of “degrading and ultimately defeating” Isis, Obama’s stated goal.

Dempsey and Hagel, who described the US as being “at war” with Isis, were more thorough to the committee about US strategy in Iraq than against Isis in Syria, where Dempsey said “two-thirds” of its estimated 31,000 fighters currently are.

In Iraq, the US intends to build upon the 162 air strikes it has launched since August 8, in support of Iraqi and Kurdish ground forces’ efforts to take Iraqi territory away from Isis and “restore the border” with Syria, Dempsey said.

In Syria, the US is seeking to train “vetted” Syrian rebels to capture Syrian territory from Isis. Hagel and Dempsey acknowledged that an initial cohort of 5,000 Syrian opposition forces would not be ready until eight months at the earliest. The House of Representatives plans to attach authorization for the training mission to a must-pass stopgap funding bill with a vote on Wednesday – which will represent the most robust congressional debate thus far on a new Iraq-Syria war.

“Five thousand is not going to be able to turn the tide, we recognize that,” Hagel said. Neither he nor Dempsey ruled out requesting additional authorities and funding for building a Syrian proxy army in the future.

Dempsey said he hopes enlist unnamed Sunni Arab nations with “very considerable” special operations forces to sustain the Syrian rebel army on the ground, possibly a reference to Qatar. He and Hagel demurred when asked by Senator John McCain, an Arizona Republican and Congress’s most prominent hawk, if the US’s new allies would receive American air cover if attacked by Syrian dictator Bashar al-Assad.

“We’re not there yet, but our focus is on Isil,” another name for Isis, Hagel said.

Dempsey – whose resignation McCain has called for, owing to the general’s reluctance to use the US military against Assad –conceded that “if we were to take [fighting] Assad off the table, we’d have a much more difficult time” persuading Syrians to join the coalition, but said the administration nevertheless has an “Isil-first strategy”.

McCain said relying on the Syrian opposition to prioritize fighting Isis ahead of Assad, their primary foe, pointed to a “fundamental fallacy” in the Obama administration’s strategy.

On Wednesday, Obama will meet with Austin in Tampa, where Central Command is headquartered. Hagel said the general will brief Obama on upcoming “targeted actions against [Isis] safe havens in Syria”, the clearest signal yet of an imminent expansion of air strikes into Syria. On the targeting list, Hagel said, are Isis “command and control, logistics capabilities, and infrastructure”.

Dempsey said introducing US ground forces into Syria in support of its proxy rebel army would not yield lasting gains, part of his argument that defeating Isis – the administration’s stated ultimate goal – will only result from a “generational” decision by regional Sunni Arabs to reject its ideology.

“I don’t think that even if we were to go in on the ground, armored divisions with flags unfurled, I don’t think we would do anything more than push this problem further to the right,” Dempsey told Senator Lindsey Graham, a South Carolina Republican.

“If we don’t get the kind of coalition I’m describing, then we’re into a very narrow CT framework, in my view,” Dempsey said, referencing frequent but intermittent drone strikes against counterterrorism targets the US has launched in Pakistan, Yemen and Somalia.

Some senators of both parties expressed discomfort with Obama’s willingness to involve the US in a new war ahead of explicit congressional authorization. Deb Fischer, a Nebraska Republican, and Joe Manchin, a West Virginia Democrat, both said Congress should not end its pre-election session this month without a war vote. Manchin was one of relatively few senators on the panel who appeared inclined to vote against the latest US war in the Middle East.