Middle East
16 September 2014
Last updated at 12:44 ET
The US earlier carried out its first air strike under the strategy, which seeks to "degrade and destroy" IS.
The jihadists control huge areas of Syria and Iraq.
Meanwhile, Kurdish peshmerga forces backed by US surveillance jets and drones have been advancing against IS positions in northern Iraq.
An attack into the IS-held plain of Mosul, east of the city, began at dawn while on the other side of Mosul, the Kurds have also been pressing towards the town of Zumar.
'At war' Gen Dempsey said that he believed that an international coalition against IS was currently the "appropriate way forward".
However, he said "if that fails to be true, and there are threats to the United States, then I of course would go back to the president and make a recommendation that may include the use of US military ground forces".
He confirmed that under the current plan, US military advisers would help the Iraqi army to plan attacks against IS.
He added that in certain instances, US advisers could accompany Iraqi troops.
"To be clear, if we reach the point where I believe our advisers should accompany Iraqi troops on attacks against specific Isil [Islamic State] targets, I will recommend that to the president," he said.
Jim Muir, BBC News, Irbil
Visits to two widely separated active fronts where the Kurds
are pushing back against IS show that a combination of Western air power
and motivated, cohesive local forces on the ground can turn the tide
against the militants.
A dawn offensive by Kurdish peshmerga forces at the village of Hassan al-Sham, west of Kalak on the main highway between Erbil and Mosul, marked the first push by the Kurds along that axis towards Iraq's second city, held by the militants since June.
Far away on the other side of Mosul, the Kurds were also closing in on the strategic town of Zumar, which fell to IS early last month when it suddenly stormed into Iraqi Kurdistan.
But on both fronts and elsewhere, progress has been painfully slow, in contrast to the breathtaking speed with which the militants overran large tracts of territory.
A front-line Kurdish commander at Zumar admitted that IS had "good techniques", offering few identifiable targets, melting away, striking back without warning, leaving numerous bombs and booby-traps behind, and using snipers to deadly effect.
Significant though Kurdish gains have been, they illustrate the magnitude of the challenge involved in trying to uproot IS from other extensive parts of Iraq and Syria, where the situation on the ground is much more complex.
"Given a coalition of capable, willing regional and
international partners, I believe we can destroy Isil in Iraq, restore
the Iraqi-Syrian border, and disrupt Isil in Syria" he added.
General Dempsey was testifying alongside defence secretary Chuck Hagel at the Senate Armed Services Committee.
"We are at war with Isil, as we are with al-Qaeda", Mr Hagel said.
Activists from anti-war group Code Pink heckled the officials throughout their hearing
More than 30 countries have now pledged to support Iraqi troops against IS
He outlined in more detail the US strategy for dealing with the group.
"This plan includes targeted actions against Isil safe havens in Syria, including its command and control, logistics capabilities, and infrastructure," he said.
Both men were heckled by anti-war protesters inside the chamber.
Meanwhile, Iraq's new prime minister saw his two nominations for defence and interior minister rejected by parliament.
The rejections of the two key posts are a setback for Prime Minister Haider al-Abadi.
by Sunita Kureishi, Melissa Gruz, and Biodun Iginla, BBC News
The BBC's Jim Muir is on the ground with Kurdish troops
US
ground forces could be deployed against Islamic State (IS) militants if
the current US-led strategy fails, top US General Martin Dempsey has
said.
President Barack Obama has repeatedly said that US ground
troops would not have a combat mission in Iraq under the strategy
outlined last week.The US earlier carried out its first air strike under the strategy, which seeks to "degrade and destroy" IS.
The jihadists control huge areas of Syria and Iraq.
Meanwhile, Kurdish peshmerga forces backed by US surveillance jets and drones have been advancing against IS positions in northern Iraq.
An attack into the IS-held plain of Mosul, east of the city, began at dawn while on the other side of Mosul, the Kurds have also been pressing towards the town of Zumar.
'At war' Gen Dempsey said that he believed that an international coalition against IS was currently the "appropriate way forward".
However, he said "if that fails to be true, and there are threats to the United States, then I of course would go back to the president and make a recommendation that may include the use of US military ground forces".
He confirmed that under the current plan, US military advisers would help the Iraqi army to plan attacks against IS.
Gen Martin Dempsey says he would consider deploying US military advisers in Iraq if necessary
"To be clear, if we reach the point where I believe our advisers should accompany Iraqi troops on attacks against specific Isil [Islamic State] targets, I will recommend that to the president," he said.
A dawn offensive by Kurdish peshmerga forces at the village of Hassan al-Sham, west of Kalak on the main highway between Erbil and Mosul, marked the first push by the Kurds along that axis towards Iraq's second city, held by the militants since June.
Far away on the other side of Mosul, the Kurds were also closing in on the strategic town of Zumar, which fell to IS early last month when it suddenly stormed into Iraqi Kurdistan.
But on both fronts and elsewhere, progress has been painfully slow, in contrast to the breathtaking speed with which the militants overran large tracts of territory.
A front-line Kurdish commander at Zumar admitted that IS had "good techniques", offering few identifiable targets, melting away, striking back without warning, leaving numerous bombs and booby-traps behind, and using snipers to deadly effect.
Significant though Kurdish gains have been, they illustrate the magnitude of the challenge involved in trying to uproot IS from other extensive parts of Iraq and Syria, where the situation on the ground is much more complex.
General Dempsey was testifying alongside defence secretary Chuck Hagel at the Senate Armed Services Committee.
"We are at war with Isil, as we are with al-Qaeda", Mr Hagel said.
Activists from anti-war group Code Pink heckled the officials throughout their hearing
More than 30 countries have now pledged to support Iraqi troops against IS
"This plan includes targeted actions against Isil safe havens in Syria, including its command and control, logistics capabilities, and infrastructure," he said.
Both men were heckled by anti-war protesters inside the chamber.
Meanwhile, Iraq's new prime minister saw his two nominations for defence and interior minister rejected by parliament.
The rejections of the two key posts are a setback for Prime Minister Haider al-Abadi.
Islamic State
Features and Analysis
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Will Obama's strategy to tackle IS work?Allied questions
-
Syria crucial
-
Vote or veto?
-
Hostages held by IS
-
Sunnis ready to take on IS
-
Turkey and IS
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