(CNN) -- Dozens of people have died in Pakistan and India's northern Rajasthan state amid flash floods and landslides caused by heavy monsoon rains, officials said Thursday.

At least 21 deaths are confirmed in Pakistan, said Maj. Iftikhar Ahmed Taj of the National Disaster Management Authority.

Hundreds of homes have been damaged in the flooding, which has hit parts of Punjab, Khyber Pakhtunkhwa, the Federally Administered Tribal Areas, and Pakistani-controlled Kashmir, he said.

Rescue workers are seeking to deal with a major landslide in the Kashmiri city of Muzaffarabad, according to the disaster agency.

Roads are blocked, some 390 houses have been damaged and an unknown number of people are dead and injured, the agency said. Some families trapped by the landslide have been given emergency food and water supplies.

Elsewhere in Pakistani-controlled Kashmir, seven people were killed in Bagh by a flash flood and a landslide, while more than 100 houses were damaged in Koti, the disaster agency said.

More rainfall is on the way in Pakistani-controlled Kashmir, Punjab, Khyber Pakhtunkhwa, some isolated places in northeast Balochistan, and the country's capital, Islamabad, according to the agency.

Clean-up also was under way Thursday in neighboring India, where heavy rain in Rajasthan left 20 dead, the Rajasthan state department told CNN. Ten died in the capital, Jaipur, it said.

Relief work is under way to help the hundreds of people made homeless by the flooding, which followed three or four days of heavy rain, the state department said.

Rajasthan Gov. Margaret Alva visited the affected area Thursday and spoke with people living in the slums of Madrampura Basti, the local government said in a statement.

She directed local authorities to make sure water is pumped out of people's homes and food and drinking water are made available, it said.

Meanwhile, Pakistani Prime Minister Raja Pervez Ashraf expressed his regret to those affected by the floods.

He released a statement directing government agencies to monitor river levels and take action to prevent any from bursting their banks.

The prime minister also instructed authorities to check that the early warning system for people living near rivers is kept up to date, and urged disaster management agencies to ensure they are fully prepared to respond.