"If we reach the point where I believe our advisers should accompany Iraqi troops on attacks against specific [Isis] targets, I'll recommend that to the President," Dempsey said.
Meanwhile, Congress is expected to vote this week to provide US$500 million ($610 million) in support of Syrian rebels.
Dempsey's words raise the spectre of "mission creep", with US forces being dragged further into a foreign conflict, and is likely to alarm the American public, which is firmly opposed to ground troops returning to the Middle East.
They also appear to contradict President Barack Obama's definitive promise to a war-weary country that the campaign against Isis "will not involve American combat troops fighting on foreign soil".
Dempsey and Chuck Hagel, the US Secretary of Defence, also urged Congress to provide arms and training for the moderate Syrian rebels, saying 12,000 rebel fighters would be needed to confront Isis in Syria.
The two men appeared before a Senate hearing after US aircraft attacked jihadist fighters outside of Baghdad, in their first strike since Obama expanded the American mission in Iraq. Dempsey faced questions from sceptical senators on whether Iraqi forces or the Syrian rebels would be able to roll back the gains made by Isis.
Deviating from the White House script, the general outlined a number of situations in which US troops could be sent to the front line in an advisory or support role. If Iraqi or Kurdish troops were poised to retake Mosul, Iraq's second largest city, "it could very well be part of that particular mission to provide close combat advising or accompanying for that mission", he said.
He also conceded that commanders had already suggested using US special forces to guide air strikes, but that so far none had been ordered in.
Both missions would put US troops in proximity to Isis fighters, even if they were not directly involved in combat.
Dempsey acknowledged that ground troops were not part of the policy Obama laid out to the American public in a speech last week.
"At this point his stated policy is that we will not have US ground forces in direct combat," Dempsey said.
"But he has told me as well to come back to him on a case-by-case basis."
Yesterday al-Qaeda branches in Yemen and North Africa issued an unprecedented joint statement calling for jihadists in Iraq and Syria to unite against the common threat from a US-led coalition.
Al-Qaeda in the Arabian Peninsula and Al-Qaeda in the Islamic Maghreb urged their "brothers" in Iraq and Syria to "stop killing each other and unite against the American campaign and its evil coalition that threatens us all".
School subjects banned
National history, literature, art, music and evolution have been banned as school subjects in Mosul, the largest Iraqi city under the control of Isis, under a new decree.
A document drawn up by the radical group's education department, headed by a 30-year-old religious scholar, has demanded that teachers adopt a strict Sharia curriculum for the forthcoming academic year. Any topic relating to non-Sunni Islam religious teaching is forbidden, and Christian schools have been renamed.
As the so-called caliphate is supposed to be a border-free empire of the Muslim world, anything relating to Iraq's history, culture or literature is also ruled out.
Science is permitted, so long as it does not conflict with a literalist interpretation of religious teaching.
Local news websites say many children have been kept away from school by their parents in protest.
- AFP
