Hardliners rounded on President Hassan Rouhani yesterday after negotiators failed to end the Iranian nuclear dispute but the man who ultimately matters, the country’s supreme leader, tacitly backed a renewed push for a deal.

Iranians faced the prospect of at least several more months of international sanctions that have badly hurt their living standards, after Tehran and six world powers missed a self-imposed deadline on Monday for a nuclear settlement.

But Supreme Leader Ayatollah Ali Khamenei gave his blessing after negotiators in Vienna allowed themselves seven more months to overcome the deadlock over the nuclear programme, which the West fears has military aims despite Tehran’s denials.

This extension keeps alive hopes among Rouhani’s supporters of an eventual deal that would shore up the power of the 66-year-old lawyer and cleric, an unashamed pragmatist, and possibly lead to wider economic and social reform at home.

After Rouhani soundly beat conservative rivals to win a presidential election last year, the hardliners were unlikely to be happy whatever the outcome of the negotiations with the US, China, Russia, France, Britain and Germany. They remain suspicious of reaching any compromise with the West, after Rouhani promised during campaigning to end the sanctions by resolving the nuclear dispute and re-engaging Iran with the outside world.

But equally they demanded explanations from Rouhani about why a year of talks that he helped to arrange had failed to produce a compromise by Monday, the second deadline to have been missed.

Chants of “Death to America”, a slogan Rouhani’s sympathisers avoid using, punctuated a meeting of lawmakers yesterday.

“It’s already a year since Rouhani tried his magic key to turn around America’s wolfish nature. Instead of turning, the key of trust and optimism broke in the lock,” said Hamid Rasaei, a member of Parliament and close ally of hardline ex-president Mahmoud Ahmadinejad.

“We have no idea what happened in Vienna ... What has been agreed upon in Vienna?” he asked on the floor of the assembly.

Rouhani told state TV that progress had been made in the talks, an assertion backed by US Secretary of State John Kerry, and that he was sure a deal would be concluded one day. But conservatives tried to cast Rouhani’s government as insufficiently robust in its stance on the nuclear work, a damaging charge if his opponents could make it stick.