Rouhani refuted the calls for the resignation of his government, official IRNA news agency reported.
"Thanks to the guidance of the Supreme Leader and supports of the nation, we are moving in the path of national interests," Rouhani said.
"If somebody thinks the government will resign, he makes a mistake," he added.
The Iranian president also lashed out at the mounting US pressures on the Islamic republic.
"No Iranian will surrender to pressures, oppression and insults," Rouhani vowed.
Following US President Donald Trump's decision to quit the historic Iran nuclear pact on May 8, Washington vowed to re-impose sanctions against Iran and inflict punishments, including secondary sanctions, on countries that have business links with the Islamic republic.
Major international energy and industrial firms have since left Iran to avoid the risks of the US punishments.
Earlier in the day, Mahmoud Vaezi, Rouhani's chief of staff, raised the possibility that there would be reshuffle of the government, according to Tasnim news agency.
"We will have some changes in the cabinet," Vaezi said. "This administration will have changes in the cabinet for the sake of dynamism, but it is up to the president and I do not know when it will happen."
The reports about cabinet reshuffle came after a special meeting held by the government officials over the fall of the national currency.
The Iranian rial plunged to a record low against the US dollar on the unofficial market on Sunday.
One dollar was being offered for as many as 87,000 rials, compared to around 75,500 on Thursday, the last trading day before Iran's weekend, according to foreign exchange websites, which track the unofficial market.
The collapse of the national currency has provoked a public outcry over the rocketing prices of imported consumer goods.
Over the past days, protests against soaring prices and unstable currency rate gripped the Grand Bazaar of the capital Tehran, which led to the closure of businesses there.
Tehran Prosecutor General Abbas Jafari Dolatabadi said on Tuesday that Iranian security forces arrested suspects in the unrest, who will remain in custody pending trial.
On Wednesday, an Iranian oil official told Tasnim that the US efforts to ban Iran's oil exports will be futile as it is not an easy task to block the country's crude from the global market.
Although some European companies, such as Shell and Total, have stopped buying Iranian oil over the past few weeks, Iran is still exporting oil to Europe, Asia and elsewhere in the world, Tasnim news agency cited the unnamed Petroleum Ministry official as saying.
A day earlier, a senior US State Department official told reporters that the United States has been pushing its allies to stop oil imports from Iran by Nov. 4.
"This big claim (of cutting Iran oil supply) is not feasible. Last month, Iran exported 2.8 million barrels of crude oil and condensate per day," the Iranian official said.
"Removing this from the global market in a few months is not possible," the Iranian official said.
However, "Iran is prepared for the worst-case scenarios" in case the US pressures take effect, he noted.
Meanwhile, "there is no surplus capacity for countries such as Saudi Arabia and the United Arab Emirates to supply oil for a long term," the official pointed out.
Besides, Maj. Gen. Yahya Rahim Safavi, a top military adviser to Iran's Supreme Leader, said on Wednesday that all Iranians are duty-bound to help the government overcome economic problems in the country, according to Press TV.
"It is our duty to work in coordination and synergy to help the government and other branches overcome economic woes and foil enemy plots for an economic war and psychological warfare," Safavi said.
He expressed hope that the Iranian nation would surmount the difficult economic conditions imposed by the enemy through the unity of the people and government institutions.