At least 10 people were killed and dozens injured in three separate accidents involving trains in the fog-bound northern Indian state of Uttar Pradesh on Saturday, police and railway officials said.

In the first accident, an inter-city express rammed into the back of a stationary passenger train near the town of Sarai Bhupat, 250 kilometres (155 miles) southwest of the state capital Lucknow.

Additional police director general Brij Lal said 10 passengers were injured including three whose condition doctors described as "grave."

Ten people were killed in the second accident 45 minutes later when two other express trains collided in similar fashion, around 80 kilometres (50 miles) southwest of Lucknow, Lal said.

Three of those killed were women, rail officials at the accident site said.

"We have rushed 37 injured passengers to hospitals but the condition of 12 of them is critical," officer Lal told AFP.

Senior railways official M.N. Srivastava said the impact in both train collisions had been minimised by the fact that the trains were travelling at low speeds because of the dense fog.

In a third accident, a passenger train slammed into a tractor at an unmanned rail crossing, officer Lal said, adding that three people on the tractor were injured in the mishap, near Allahabad city, also in Uttar Pradesh.

There were no injuries to passengers on the train, he said.

Visibility at the three accident sites was down to around 30 metres (100 feet).

The string of accidents threw train services into disarray across India, rail officials said in New Delhi.

Obsolete safety measures and unmanned crossings result in frequent rail accidents in India, where more than 13 million people travel on state-run railways every day.