The flooding has left at least 1,500 people dead and thousands stranded, local media reported.
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Several countries and charities have promised to send aid, and the Pakistani army is using helicopters to deliver food, aid supplies and tents. Relief work has been hampered because of washed-out bridges, flooded roads and downed communication lines.
Canada pledged Tuesday to provide $2 million in humanitarian assistance to Pakistan, including $1.25 million for emergency food assistance through the World Food Program.
International Co-operation Minister Bev Oda said the contribution will go to help more than 150,000 families affected by the floods.
The funds will be distributed through the Canadian International Development Agency, with $750,000 also going to the International Federation of the Red Cross and Red Crescent Societies, Oda said in a release.
UNICEF said roughly three million people were affected by the floods, which knocked down homes and wiped out crops.
David Morley, the CEO of Save the Children Canada, said relief workers and health teams are struggling to reach remote communities that have been hit by floods.
"We have health teams that need to get rafts that are attached to pulleys, just to get across some of the swollen rivers to be able to reach the clinics [and] the villages," Morley said.
He worries that the situation could worsen in the coming days as more rain falls and floodwaters move south.
Waterborne disease a risk
As flood waters wash away communities and contaminate water supplies, officials are expressing concern about possible outbreaks of waterborne diseases.
"There are crucial needs for food and safe drinking water," UNICEF representative in Pakistan Martin Mogwanja said in a statement. "Potential disease outbreaks among survivors are a major concern."
International medical relief organization Médecins Sans Frontières (Doctors Without Borders) is distributing clean water in Swat and has set up two cholera treatment centres in case there is an outbreak.
Cholera is intestinal infection transmitted through food or water contaminated with the bacterium Vibrio cholerae, the World Health Organization says. Most people infected with cholera don't get sick, but it can cause vomiting, watery diarrhea and dehydration.
The flooding has destroyed at least 39 health facilities and many hospitals are short on supplies, the WHO says.
"What they need is money," said Sallah Hamdani, the executive director of Islamic Relief Canada. "They need money in order to buy supplies on the ground."
Emilia Casella, a spokeswoman for the UN's World Food Program, said the agency had delivered food to 40,000 people and is aiming to reach 250,000 people by the end of the week.
But "access is really remaining a major challenge," she said.
New flood warnings
Officials issued new flood warnings Tuesday as more rains fell and rising water levels threatened to overwhelm the Warsak Dam, one of the country's biggest dams.
The rising water levels prompted disaster officials to ask residents in the northern outskirts of Peshawar city to leave their homes.
"If needed, forced evacuation will be started," said Adnan Khan, a spokesman for the Disaster Management Authority of Khyber-Pakhtoonkhwa province.