NEW DELHI, May 7 (Reuters) - India reported another record daily rise in coronavirus cases on Friday, bringing total new cases for the week to 1.57 million, as the country's vaccination rate falls dramatically due to a lack of supplies and transport problems.

As India's deadly second wave of COVID-19 continues unabated and its total number of cases now stand at 21.49 million, with infections spreading from overcrowded cities to remote rural villages that are home to nearly 70% of the 1.3 billion population.

The country reported a record daily 414,188 new cases on Friday, while deaths from COVID-19 swelled by 3,915, bringing total deaths to 234,083.

Medical experts say the real extent of COVID-19 in India is five to 10 times the official tallies.

Prime Minister Narendra Modi has been widely criticised for not acting sooner to suppress the second wave, after religious festivals and political rallies drew tens of thousands of people in recent weeks and became "super spreader" events.

His government has also been criticised for delays in the country's vaccination programme, which medical experts say is India's only hope of controlling the second COVID-19 wave.

The Hindustan Times newspaper on Friday demanded: "Accelerate the vaccine drive, get the second wave of the pandemic under some control..."

While India is the world's biggest vaccine maker, it is struggling to produce enough doses to stem the wave of COVID-19.

Modi has stressed that Indian states must keep up vaccination rates. Although the country has administered at least 157 million vaccine doses, its rate of inoculation has fallen sharply in recent days.

"After having achieved a rate of around 4 million a day, we are now down to 2.5 million per day due to vaccine shortages," Amartya Lahiri, an economics professor at University of British Columbia was quoted as saying in the Mint newspaper.

"The 5 million a day target is the lower bound of what we have to aim for, since even at that rate, it will take a year for us to get everyone two doses. The situation unfortunately is very grim."