The future of the World Trade Organisation has been thrown into doubt after eleventh-hour attempts to salvage a global trade deal collapsed.

Talks broke down after India's refusal to back a deal unless it included concessions allowing developing countries freedom to subsidise and stockpile food.

An agreement on the deal, centred on loosening global customs rules, had been reached in Bali in December, with a deadline of midnight on Thursday to ratify it. But it was scuppered after the WTO's 160 members failed to reach agreement over India's demands.

It would have been the first global trade deal reached by the Geneva-based institution since it was founded almost two decades ago. The last-minute failure to reach agreement prompted questions over the very existence of the WTO and how it will survive the deadlock.

Admitting defeat, Roberto Azevêdo, the director general, was candid about the challenges facing WTO. Despite intense negotiations, disagreement between members had not been resolved, he said.

"We have not been able to find a solution that would allow us to bridge that gap. We tried everything we could. But it has not proved possible," he said. "The fact we do not have a conclusion means that we are entering a new phase in our work – a phase which strikes me as being full of uncertainties."

Speaking about the future of the organisation, Azevêdo said: "What this means for the WTO will be in the hands of the members. I think we should take the time to reflect and come back in September."

Created in 1995, the WTO was set up to help trade flow smoothly and freely around the world. It describes its main tasks as facilitating trade negotiations and handling trade disputes.

But experts say failure on this key agreement risks consigning it to the status of a referee for disputes and could see it ceasing to exist as a forum for serious trade liberalisation talks.

The US was quick to reproach India for its refusal to sign the trade deal. The US secretary of state, John Kerry, on a visit to New Delhi, told India's prime minister, Narendra Modi, that his country's actions sent the wrong signal.

"Failure to sign the trade facilitation agreement sent a confusing signal and undermined the very image prime minister Modi is trying to send about India," a US state department official told reporters after Kerry's meeting with Modi.

Other WTO members publicly voiced their frustrations.

"Australia is deeply disappointed that it has not been possible to meet the deadline. This failure is a great blow to the confidence revived in Bali that the WTO can deliver negotiated outcomes," said Australian trade minister Andrew Robb. "There are no winners from this outcome, least of all those in developing countries which would see the biggest gains."

For its part, India sought to reassure fellow WTO members it was willing to return to the table. A senior trade ministry official told Reuters that India was prepared to engage with the other countries to sign a deal in September. But the country again demanded that its calls for concessions on stockpiling food be granted. Azevêdo stressed that any resurrection of the talks relied on the will of WTO members.

"I remind you that 31 July is not my deadline — it is a Bali deadline decided by ministers – and a deadline that many delegations have made clear we must observe," he said, urging WTO delegates to go back to their governments at the "highest possible level" and "stress the importance of the situation we find ourselves in".

"The future of the multilateral trading system is in your hands," he said.

When the deal was hammered out in Bali, a tearful Azevêdo told the summit's closing ceremony that, for the first time in history, "the WTO has finally delivered" on large scale negotiations. But, even at the time, questions were raised about the fairness of the deal to developing nations and critics accused the pact of favouring big business at the expense of poor countries.

Some members, including the US and the European Union, have discussed trying to move forward by leaving India out of the deal.

But New Zealand's minister of overseas trade, Tim Groser, told Reuters there had been "too much drama" surrounding the negotiations and that talk of excluding India was naive and counterproductive. "India is the second biggest country by population, a vital part of the world economy and will become even more important. The idea of excluding India is ridiculous."