Earlier the Sunni insurgents launched an attack on Iraq’s biggest oil refinery at Baiji north of Baghdad.
Iraqi PM Nouri Maliki earlier urged Iraqis to unite against the militants.
Government forces are battling to push back ISIS (Islamic State in Iraq and the Levant) and its Sunni Muslim allies in Diyala and Salahuddin provinces, after the militants overran the second city, Mosul, last week.
US President Barack Obama is due to discuss the Iraq crisis with senior Congress members on Wednesday.
Ahead of the meeting Senate leader Harry Reid, a Democrat, said he did not “support in any way” getting American troops involved in the Iraqi “civil war”.
But Gen Dempsey told a Senate panel that it was in America’s “national interest to counter [ISIS] wherever we find them”.
In other developments:
- UK Prime Minister David Cameron told Parliament in London that ISIS was also plotting terror attacks on Britain
- India confirmed that 40 of its citizens had been kidnapped in the violence-hit Iraqi city of Mosul
- Saudi Foreign Minister Saud bin Faisal warned that Iraq faced the risk of civil war
- Turkey is investigating reports that 15 Turkish builders were abducted by ISIS on Tuesday; 80 Turks were kidnapped in Mosul last week