Ali Larijani, Iran's chief nuclear negotiator, delivered the response on Tuesday to foreign envoys representing the six co-sponsors of the package in Tehran, his office said.
Officials close to the meeting said Iran had offered a "new formula" to resolve the dispute, but gave no further details.
Britain, Germany, France, China, the US and Russia offered Iran a range of economic, political and security incentives in June to encourage it to stop work that could be used to make atomic bombs.
Diplomats had said they were expecting an "ambiguous" response and Tehran has indicated it would not address a key demand that it halt uranium enrichment work.
Iranian officials said the reply would pave the way for renewed talks over the dispute which began four years ago when it was revealed that Iran had been building an advanced atomic programme for almost two decades.
Mohammad Saeedi, deputy head of Iran's Atomic Energy Organisation, told the ISNA news agency: "Iran's response will provide the West with an exceptional chance for an understanding and a return to talks."
The UN security council - frustrated with Iran's slow response to the offer - has given Tehran until August 31 to halt enrichment or face possible sanctions.
Manouchehr Mottaki, Iran's foreign minister, said: "Based on negotiations, there is a possibility for a comprehensive solution to this matter."
Iran's reply - which is expected not to include a clear "Yes or "No" - could open divisions in the security council where the US, France and Britain back sanctions but Russia and China, both key trade partners of Iran, oppose them.