During the inauguration of his new foreign minister, he said one of the reasons he was elected was to change his country’s foreign policy.
But he said this did not mean Iran abandoning its principles.
The country’s outgoing nuclear chief later said Iran boasted about 18,000 centrifuges for uranium enrichment – of which 10,000 were operational.
Fereydun Abbasi-Davani’s announcement came as he handed over his post as head of the Atomic Energy Organisation of Iran (AEOI) on Saturday to former Foreign Minister Ali Akbar Salehi, appointed by Mr Rouhani.
The operational centrifuges are of the older IR1 type, with a further 7,000 ready to be installed along with 1,000 centrifuges of the advanced IR2m type.
Iran’s nuclear programme has been the subject of a sustained diplomatic tussle with Western powers, who say they suspect it is aimed at developing nuclear weapons.
Iran rejects this, saying its programme is purely civilian.
But its new leader – the surprise victor of the elections held on 14 June – has pledged to pursue “serious” talks with the West to ease tensions and in so doing improve an economy hit hard by international sanctions and internal mismanagement.
Foreign policy ‘key’
On Saturday, President Rouhani implied that he would move away from the bombastic style of his predecessor, Mahmoud Ahmedinejad.
“Foreign policy is not carried out by repeating slogans,” he said.
“One of the messages of the voters in the presidential election was that they wanted a change in foreign policy,” the ISNA news agency quoted him as saying at the inauguration of the new Foreign Minister, Mohammed Javad Zarif.
“That doesn’t mean abandoning our principles but it does mean a change of method.
“We are going to strongly defend our national interests but that has to be done appropriately, precisely and rationally,” the president said.
“The public will pay dearly for any foreign policy mistake.”
Foreign policy was “key to solving our current problems”, Mr Rouhani said.
Mr Rouhani took office on 4 August and on Thursday all but three of his 18 cabinet choices were approved by parliament. Many of those new ministers have lived or been educated in the West, as has the president himself.