India says it has become the "fastest country in the world" to administer more than 100 million doses of coronavirus vaccines, amid a deadly second wave of infections.

It achieved the feat in 85 days, whereas the US took 89 days and China 102 days, the health ministry said.

But the country reported a record daily increase of over 150,000 cases - and more than 800 new deaths - on Sunday.

And there are reports the vast vaccination drive itself is struggling.

This week, half a dozen states reported a shortage of doses even as the federal government insisted that it had 40 million doses in stock and that the "allegations" of vaccine scarcity were "utterly baseless".

The inoculation drive aims to cover 250 million people by July, but experts say the pace needs to pick up further to meet the target.

Everyone aged over 45 is now eligible for jabs at vaccination centres and hospitals. Most doses have so far been given to frontline workers and the over-60s.+

The third phase - which began on 1 April - opened amid a sharp uptick in Covid-19 cases. India has been reporting an average of more than 90,000 cases every day since then.

On 4 April, India became the second country after the US to report 100,000 new cases in a single day. More than half of those were confirmed in Maharashtra, which has India's largest city Mumbai as its capital.

India's caseload had dropped sharply by the time it began vaccinating people early this year. It was adding under 15,000 infections daily. But cases began to spike again in March, largely driven by poor test-and-trace and lax safety protocols.

Experts say India's second wave is being fuelled by people being less cautious - and mixed messaging by the government.

Since the pandemic began, India has confirmed more than 12 million cases and over 167,000 deaths. It's the third-highest number of Covid-19 infections in the world after the United States and Brazil.

How is the rollout going?

India launched its vaccination drive on 16 January, but it was limited to healthcare workers and frontline staff - a sanitation worker became the first Indian to receive the vaccine.

From 1 March, the eligibility criteria was expanded to include people over 60 and those aged between 45 and 59 with other illnesses.

The third phase included everyone above the age of 45.

The country's drugs regulator has given the green light to two vaccines - one developed by AstraZeneca with Oxford University (Covishield) and one by Indian firm Bharat Biotech (Covaxin). Several other candidates are at different stages of trials.

India also wants to scale up the drive quickly to stem the recent spike in cases. So it placed a temporary hold on all exports of the Oxford-AstraZeneca coronavirus vaccine, which is being made by India's largest vaccine manufacturer, the Serum Institute of India (SII).

The vaccine maker recently said its production capacity was "very stressed" and that it was "still short of being able to supply to every Indian".

Serum says it has been providing 65-70 million doses every month to India, and exported nearly an equal amount since it began production early this year.

The firm was aiming to boost production to 100 million doses a month. Now it says it would not be able to meet that target before the end of June because of time taken to repair damages from a fire at its facilities in the western city of Pune in January.

Experts believe India should ramp up vaccination in areas of high transmission and in five states where elections are being held.

Dr Murad Banaji, a mathematician at Middlesex University London who is closely tracking the pandemic, told the BBC that he hoped vaccinations would play a part in controlling the second wave.

"But at the current pace, vaccination is going to have little effect on slowing spread in a month or two. Being targeted at the most vulnerable, it might, however, start reducing hospitalisations and deaths more quickly."

Bhramar Mukherjee, a biostatistician at the University of Michigan, told the BBC that India needed to administer 10 million shots daily "instead of being complacent with three million" doses a day.

"I do feel frustrated that India did not roll out the vaccination drive more aggressively while the curve was in its valley," Dr Mukherjee said.

"It is much easier to roll out vaccination when the infection is not so high. Now the healthcare capacity is stretched between vaccination and Covid care."

How many have been vaccinated so far?

India has administered more than 100 million doses of coronavirus vaccines so far.

For decades now, the country has been running one of the world's largest immunisation programmes that vaccinate tens of millions, including newborns and pregnant women, against various diseases.

So experts believed India was well-prepared for the challenge. But the uptake has been slow because of vaccine scepticism as well as a lack of awareness among the poor or in rural areas.

Many of the poor have little information on how to register themselves and access the vaccine free of cost. Eligible people can now book their jabs online or walk in and register at vaccination centres.

"There's very little public health communication for the poor and the working class regarding the vaccines," says Radha Khan, an independent consultant working in the field of gender, governance and social inclusion.

The government aims to use up to 500 million doses to cover 250 million "priority people" by the end of July.

Interestingly, in some states, more women than men have been vaccinated. The reasons are not clear.

Who is paying for the vaccines?

Vaccination is voluntary. State-run clinics and hospitals are offering free jabs, but people can also pay 250 rupees ($3.4; £2.4) a dose at private facilities.

Starting 11 April, people can get paid jabs at private and state-run workplaces.

The government is spending around $5bn to provide free doses at state-run clinics, public health centres and hospitals.

It has also bought millions of doses of two approved vaccines and provided funds to states for their vaccination programmes.

Have there been 'adverse events' after vaccination?

People can experience side effects from vaccines.

India has a 34-year-old surveillance programme for monitoring "adverse events" following immunisation. Experts say a failure to transparently report such incidents could lead to fear-mongering around vaccines.

Until early February, India reported 8,483 "adverse events" after vaccination. Most of these events were "minor" - anxiety, vertigo, giddiness, dizziness, fever, and pain - and all patients had recovered, the government said.

The surveillance programme has examined 617 cases of "severe adverse events", including 180 deaths after vaccination until 29 March, according to reports.

It found the "deaths happened in cases where the person had underlying conditions, including heart problems, high blood pressure and diabetes".