President Hassan Rouhani said Sunday that sceptics who had warned a nuclear deal with world powers would not bring benefits to Iran "were all proven wrong".

"Within a few hours" of the nuclear deal being implemented and sanctions lifted "1,000 lines of credit were opened by various banks," Rouhani told reporters in Tehran.

"This showed that those who used to say, 'do not believe' were mistaken," he said, stressing the deal would now make it easier for Iranian businesses to operate after years of being frozen out of the international financial system.

"Today we are in an atmosphere where we can have political, economic and legal interaction with the world to the benefit of our national interests," the president said.

"We believe in our national strength. We believe in our nation's success," he added.

The remarks were a riposte to doubters who say that the diplomatic success of the nuclear deal will not translate into concrete economic benefits for Iran's economy.

Rouhani staked his presidency on the nuclear talks, deepening the diplomacy which involved Britain, China, France, Russia and the United States plus Germany after taking office in August 2013.

Only last week he said Iranians should look forward to a "year of prosperity" after sanctions are lifted.

Rouhani also hit out at Saudi Arabia's criticism of the nuclear deal, citing an unnamed official who said the removal of sanctions was a bad development.

"On the day of implementation we saw one Saudi official express regret that Iran's economic problems have been solved," the Iranian president said.

"A neighbour would never behave this way. A Muslim would never act this way. A Muslim would not be upset over another Muslim's comfort. Muslims are all brothers," he said.

Following the Sunni kingdom's execution of Shiite cleric Nimr al-Nimr on January 2, Saudi Arabia's embassy in Tehran was ransacked -- an act condemned by Rouhani.

Saudi Arabia severed diplomatic relations a day later.

Rouhani said the door was still open to diplomacy but it would not stay open forever.

"What we want is to resolve regional issues through logic but at the same time, our people, our government will not accept non-diplomatic and inappropriate behaviour," he said.

"If it's necessary, a firm response will be given, but we hope... that they will move toward a direction which will be in the interest of the region and their own people."