The comments come ahead of meeting later this month between his Foreign Minister Mohammad Javad Zarif and EU foreign policy chief Catherine Ashton on restarting negotiations on the Islamic republic's disputed nuclear ambitions.
"Our government will not give up one iota of its absolute rights" on the nuclear issue, said Rowhani, a reputed moderate, repeating a mantra frequently used by his predecessor Mahmoud Ahmadinejad.
Soon after his election as president in June, Rowhani promised more transparency, saying he wanted "serious" talks with world powers to resolve Western suspicions that Iran's nuclear drive is cover to build a bomb despite repeated denials by Tehran.
The two sides have failed to achieve a breakthrough in years of talks, with Iran - during Ahmadinejad's two-term presidency -- refusing to make any concessions on sensitive activities in the nuclear programme, notably uranium enrichment.
That has led to several rounds of international sanctions being slapped on the Islamic republic, crucially targeting its oil sector and access to the global banking system, choking the economy and stoking a raging inflation.
The last round of talks between Iran and the so-called P5+1 of world powers ended in Almaty in April with an impasse.
In parallel diplomatic efforts, the International Atomic Energy Agency (IAEA) is urging Iran to provide necessary cooperation to remove suspicions it seeks a nuclear weapons capability.
A new round of talks between Iran and the Vienna-based UN watchdog is set for September 27.
"Given the nature and extent of credible information available to the agency about possible military dimensions to Iran's nuclear programme, it remains essential and urgent for Iran to engage with us on the substance of these concerns," IAEA chief Yukiya Amano said Monday.
Iran was accused of unsatisfactory cooperation with the IAEA when Ahmadinejad was in office.
Himself a former nuclear negotiator, Rowhani on Tuesday did not elaborate on efforts to resolve such concerns over Iran's nuclear programme, on which all final decisions - like other key issues in the Islamic republic - rest with the country's supreme leader, Ayatollah Ali Khamenei.
But he warned pressure would not make Iran abandon its rights.
"The West must understand that it will not obtain any result by threats and pressure," he stressed.
Rowhani added that after the Zarif-Ashton meeting in New York, nuclear negotiations would "continue in another place with the 5+1," which groups the United States, Russia, China, France, Britain and Germany.
He has reshuffled top officials dealing with the programme, appointing a new envoy to the IAEA, Reza Najafi, and former foreign minister Ali Akbar Salehi to head Iran's Atomic Energy Organisation.
And last week he handed responsibility for future talks with the P5+1 to the foreign ministry.
Under Ahmadinejad, the Supreme National Security Council was directly in charge of the talks, with its hardline secretary Saeed Jalili leading Iranian negotiators in several rounds of fruitless negotiations.
Jalili came under fire during the presidential election for his inability to make concessions in the talks.
And he was on Tuesday replaced by decorated admiral Ali Shamkhani, who served as defence minister under reformist president Mohammad Khatami from 1997 to 2005.
Earlier in the day, foreign ministry spokeswoman Marzieh Afkham said the council's role would not be eliminated as it would still be involved in the decision-making process.
"Decisions, as well as the framework, with regards to the nuclear negotiations will be decided in the Supreme National Security Council... (but) the foreign ministry will be in charge of the talks," she told reporters.
Rowhani, who took office early August, insists the only way to interact with the Islamic republic is through dialogue not sanctions, while ruling out any halt to the nuclear activities.