Authorities in Pakistan and India are struggling to cope with raging monsoon floods which have killed more than 460 people, displaced nearly a million people, and still threaten many more.

Pakistani military specialists blew up dykes with explosives to divert water from rivers running close to three cities, while Indian authorities admitted that relief efforts had not yet reached about 300,000 people in Kashmir.

Local people, aid-workers and medical staff in the Indian-administered parts of Kashmir criticised the relief effort, which they called "inadequate and chaotic".

Srinagar citizens escaping flooded homes on Thursday. Photograph: Haziq Qadri/The Vox Kashmir/BI

One aidworker based in Srinagar, a city of one million people, said the coordination between the Indian military, local authorities and NGOs had been "almost nonexistent".

Valay Singh, of Save the Children, said that at least 50,000 people were living in community-run relief centres, mainly mosques and Sikh temples. "People who are rescued have next to nothing, as of now. They need shelter, food, medicines clothes. There's no consolidated list of the rescued people in the relief camps. There is an urgent need to compile lists as it will help in identifying people displaced by the floods and help them in reuniting them with their families."

More than 200 people have been killed in Srinagar and bodies have reportedly been seen floating in the streets. Police said some residents of the city had been trapped in the top floors of their homes since heavy rains caused the Jhelum river to surge last week.

Volunteers in Srinagar hand out relief supplies. Photograph: Altaf Qadri/AP

Mohammad Farhan Malik, a volunteer doctor in Srinagar described a chaotic situation in the city. "There are over 20,000 people here [at one large mosque]. Most people are suffering from conjunctivitis, stress, gastroenteritis. We fear an outbreak of cholera. We have to be prepared for the worst. There are just eight to 10 doctors working ... but the government hasn't set up any proper health camp."

Water levels in Kashmir have started to drop, but the extent of destruction in more remote areas remains unclear.

"There are some villages where everything has been swept away. People are extremely angry, frustrated and exhausted," said R K Khan, an Indian police official.

The Indian air force announced on Thursday night that it had been forced to scale back operations after angry survivors pelted helicopters with stones. Most communications networks in Kashmir had failed and only 20% of the population had clean water supplies, reports in India said.

The Jhelum river flows from Indian Kashmir to the Pakistan side, then down into the flat fertile lands of Punjab. The two embankments destroyed by the army on Thursday were near the cities of Muzaffargarh and Multan. The new breaches flooded farmland and small villages.

The disaster, caused by heavy rains over the last eight days, has so far forced more than 700,000 people to flee their homes in Pakistan. Some chose to remain to protect their property and land only to end up being trapped on what few high positions they could find.

"We sat on roofs for three days waiting for help," said Allah Wasaee, a mother of 10 children, from a village near Jhang city. "Even the women climbed up into the trees to escape the water."

Nawaz Sharif, the prime minister of Pakistan, visited the Pakistan-administered portion of Kashmir on Thursday and told flood victims that his government would do whatever it could to rebuild their damaged homes.

The prime ministers of both India and Pakistan offered each other help at the weekend to deal with the disaster, which temporarily diverted attention from fighting along the national borders. The crisis is the first humanitarian emergency in India since Narendra Modi took power in India in May.

The two states have fought four wars since winning their independence from Britain in 1947 and tension over Kashmir is a key factor in the mutual hostility. This week, however, violence flared again on the "line of control", the de facto border splitting Kashmir, as Indian troops shot dead three militants even as flood rescue operations began elsewhere.

In Pakistan, hardline Sunni sectarian groups, some with a history of fighting in Kashmir, have rushed to assist families who have fled to relief camps.

Other supposedly banned groups have also been quick to extend support, including the charity arm of Jamaat-ud-Dawa, which is led by Hafiz Saeed, a controversial hardline cleric. The group has set up its own camps, as well as offered food to displaced families.

Saeed is blacklisted under the UN's international terrorism sanctions and is also subject to a $10m US bounty for his role in the 2008 assault on the Indian city of Mumbai that killed 166 people.

South Asia experiences monsoon rains from June to September, which are vital for the regional agriculture. But the rains frequently turn to floods, devastating crops, destroying homes and prompting outbreaks of diseases and diarrhoea.

Deluged streets in Srinagar. Photograph: India defence ministry/EPA

Environmentalists in Delhi said the government should recognise that floods were getting worse due to climate change.

"The Kashmir floods are a grim reminder that climate change is now hitting India harder," said Chandra Bhusan, head of the climate change team at the Centre for Science and Environment.

The International Federation of Red Cross and Red Crescent Societies said this year's monsoon rains had killed more than 1,000 people in India alone.

Disaster preparation in both countries often falls foul of bureaucratic infighting and political rivalries.

Greater Kashmir, a newspaper in Srinagar, reported that the flood control department warned in a report in 2010 that a significant flood could occur in the state within five years. The report was sent to the union water resources ministry along with plans for a £220m flood prevention scheme, the newspaper said.

In 2010 floods in Pakistan caused by the rains killed more than 2,000 people and caused huge damage.

The southern Pakistani provinces of Sindh and Balochistan are bracing themselves as the storm surge continues down the length of the country.