The rains are forecast to move north from Kerala into Karnataka

The rains hit southern Kerala state on Sunday, more than a week later than normal.

Weather officials say light pre-monsoon rains have already brought relief to some parts of the worst-hit state of Andhra Pradesh, where 1,401 deaths have been recorded.

CVV Bhadram, director of Andhra Pradesh's Meteorological Centre, said: "The weather situation is improving fast and the heat wave has subsided to a large extent."

Mr Bhadram said more showers were forecast for the next 24 hours but the full monsoon was not likely to reach the state for another week.

Tourist death

The Indian Meteorological Department said the monsoons were likely to advance north and east from Kerala, firstly into southern Karnataka state.

The department also predicted dust and thunderstorms in the northern Indian states of Punjab, Haryana, Uttar Pradesh and the desert state of Rajasthan.

Some states in the northern region, such as Kashmir, Uttaranchal and Himachal Pradesh were likely to receive rains soon, it said.

Rains have already reached many parts of the north-east.

A cyclone over Bihar and Jharkhand was causing widespread downpours, the Bihar Meteorological Office reported.

Assam, Nagaland, Manipur, Mizoram and Arunachal Pradesh also received heavy rains on Sunday.

More than a third of Bangladesh has been covered by monsoons, weather officials there said.

The heat wave was blamed for the death of an Australian woman on Saturday.

Jane Kelly, from Sydney, was travelling in a crowded train to the Hindu holy town of Varanasi when she fell ill with heat stroke, the Press Trust of India news agency said.

Meanwhile, health authorities in Pakistan say at least 250 people have died because of the extreme heat over the past two weeks in Punjab province.

Dr Javed Asghar, the Punjab chief minister's adviser on health, said the figure could be higher because information was still being compiled.

Overnight rain brought down temperatures by an average of eight degrees in Islamabad and other northern cities.