The fighting left at least seven members of one family dead or wounded on Saturday, UNHCR spokesperson William Spindler told reporters. An estimated 50,000 people remained trapped.

"They are locking some families down inside the hospital building," Salem al Halbusi, who lived in Fallujah, told USA Today. "They are making people freak out over the (arrival of) Iraqi forces by telling them, 'The army and militia are coming to kill you all.'"

Iraqi forces battling their way into the city repelled a four-hour ISIS attack in the city's south on Tuesday, a day after first moving into the southern edges of the militant-held city with the help of U.S.-led coalition airstrikes. The attack started at dawn in Fallujah's Nuaimiya area where Iraqi troops captured almost 85 percent of the ground the previous day, two officers with the special forces told The Associated Press.

Pentagon spokesman Capt. Jeff Davis described Fallujah as "the last bastion of ISIS control in Anbar Province," adding that the terrorists "intend to put up a fight." Officials told Fox there were between 500-1,000 ISIS fighters in Fallujah.