Any participation by Iran in international talks on the nuclear issue would "definitely be aimed at reinforcing" those rights, Ahmadinejad was quoted as saying in the report.
The Web site said Ahmadinejad made the remarks during discussions with Syrian President Beshar Assad, who arrived on a two-day visit.
"The Iranian nation will not give up a single iota of its nuclear rights," Ahmadinejad said.
Assad is in Tehran to discuss Iran's controversial uranium enrichment following a request from French President Nicolas Sarkozy.
Syria is Iran's closest Arab ally - the two countries have had close relations since 1980, when Syria sided with Persian Iran against Iraq in the 1980-88 Iran-Iraq war.
Assad, who has been seeking a more prominent Mideast role for Syria, promised Sarkozy during a visit to France in July to try to persuade Iran to offer proof to the West that it isn't developing nuclear weapons.
Iran's claims that it only wants nuclear technology for the production of energy have failed to quell Western suspicions that it is seeking a pathway to an atomic bomb.
Tehran was given an informal two-week deadline, set July 19 by the Security Council's permanent members plus Germany, to stop expanding uranium enrichment - at least temporarily - in exchange for their commitment to stop seeking new U.N. sanctions.
The deadline expires this weekend.
Ahmadinejad's stance signaled both a failure of Assad's mission and a rejection of the deadline, although the wording indicated he was not ruling out international talks on Iran's nuclear program.
Press Secretary Dana Perino says the U.S. will consult with its allies on the Iranian statement.
Perino, who had earlier warned of "negative consequences" if Iran rejected the United States' offer, said, "It's a shame that Iran does not take us up on our generous incentives package."
Perino's comments came in Kennebunkport, Maine as President Bush spent the weekend at the Bush family's seaside mansion.
CBS News White House Correspondent Peter Maer, who is in Kennebunkport, said Mr. Bush will be briefed on the response.
In several American cities, protests were staged against a possible U.S.-Iran conflict. In New York City, demonstrators braved heavy rain storms to gather in Times Square.
Sara Flounders, national coordinator of the Stop War in Iran coalition, said the anti-war movement's message had gained traction given the costs the Iraq War has imposed upon the U.S. economy.
"This is a nerve that we've really struck," she told CBSNews.com's Ken Lombardi. "The threat of a new war in Iran at a time of economic hardship in the U.S. - and there isn't even enough to pay for disabled veterans."
Protesters spoke of learning from the recent past.
"I can't believe we're going to make the same mistake and go back to war again," said Jared Oswald. "I don't see how another war is going to cure anything."
But anti-war protesters weren't the only ones in attendance. Counter-demonstrators waved American flags and chanted in support of President Bush and his policies.
"I'm out here because I don't want those hippies and socialists and jihadi types to be perceived as being the only ones who care enough to be out here in the rain," Eric McLaughlin told CBS News.
Meanwhile in Brussels, a European Union official said Saturday that the office of EU foreign policy chief Javier Solana had not yet received an answer from Iran but expected a reply "in the coming days" after the weekend deadline.
The official, who spoke on condition of anonymity because of the sensitivity of the issue, said EU nations and diplomats are not too concerned about Tehran's adherence to the exact deadline - but are keen for Iran to come back with a concrete reply that could form the basis of further negotiations.
Germany's Foreign Minister Frank-Walter Steinmeier urged Iran to stop playing for time and deliver a "clear answer" to the latest initiative. "Stop dallying," Steinmeier was quoted as saying in an interview with the weekly Der Spiegel that was released Saturday.
Steinmeier said he expected "a clear signal for a mutual freeze: We would freeze our sanctions efforts and Iran the development of its centrifuges." He warned it would be "negligent" for Iran to pass on the opportunity and added that in case of Tehran's refusal, the six nations would consider increasing pressure on Iran "via sanctions."
The Security Council has slapped three sets of sanctions on Iran over its enrichment and reprocessing of uranium, which can produce the ingredients for a bomb but which Tehran insists is for peaceful purposes only.
In Damascus, Syria's official news agency SANA reported on Assad's visit as having affirmed "identical views" of the two countries on "major regional and international" issues. The agency, which is a government mouthpiece, hailed the two nations' rejection of "foreign dictates" and stressed the need for a "timetable for a withdrawal of foreign forces from" Iraq - an allusion to U.S. troops there.
Assad's visit was also to focus on economic ties between Tehran and Damascus that have resulted in over a dozen projects in Syria, worth US$896 million, SANA said, adding that both governments are "seriously seeking to increase the size of joint investments to more than US$3 billion over the next years."