The Pakistani army has pressed north toward a key Taliban stronghold in the Swat District after taking control of the district capital, Mingora, on Sunday.
Pakistani troops pushed late Sunday toward the town of Charbagh, where a curfew was lifted to allow civilians to leave.
The military also dropped leaflets in the area on Sunday warning residents to evacuate ahead of a possible offensive against Taliban fighters.
Pakistani Defense Secretary Syed Athar Ali said Sunday that the offensive in Swat and surrounding districts could end within days.
On Monday, President Asif Ali Zardari ordered the release of $6 million in emergency relief funds for an estimated 2.5 million people displaced by the recent fighting.
Humanitarian workers and journalists report that the town of Mingora has been devastated, with many buildings reduced to rubble.
After completing their first assessment after the offensive, Red Cross officials said Sunday that the situation in the Swat Valley is alarming.
Daniel O'Malley, head of the Red Cross team, said people trapped in the battleground have little food, and that there is no running water, electricity or fuel for generators.
The military launched the offensive in the Swat Valley and surrounding districts last month after militants violated a peace deal and advanced within 100 kilometers of the capital, Islamabad.
The Washington Post newspaper reports that U.S. and Pakistani officials are saying that unmanned aircraft have killed about half of 20 "high value" al-Qaida and other militants operating along the Afghan border. The paper says U.S. intelligence officials believe Pakistan's offensive in the Swat Valley and the drone strikes have inflicted heavy losses on extremists and made al-Qaida worried.
Also Monday, police said a bombing at a bus terminal killed one person and killed at least five others in the northwestern garrison town of Kohat.
Some information for this report was provided by AFP and AP.