"I think they will give an answer after the G8 meeting in Saint Petersburg" scheduled for July 15 to 17, the United Nations secretary general told a press conference.

The proposal -- designed to ease international concerns that Iran's nuclear programme may be hiding atomic weapons development -- was put to Tehran by the five permanent UN Security Council members plus Germany earlier this month.

It essentially offers trade, security and technology incentives as well as talks, including with the United States, if Iran suspends uranium enrichment, which makes fuel for civilian reactors but what can also be bomb material.

"I believe it is considering their offer very seriously, as I have urged it to do, and I hope it will give its official answer before too long," Annan said.

The question of when Iran will respond is critical.

Diplomats say the United States and Europe are working toward an unofficial end-June deadline, but Iranian President Mahmoud Ahmadinejad said in a speech Wednesday that his country would respond by August 22.

US President George W. Bush retorted at a summit with EU leaders Wednesday in Vienna that that was too long. "It shouldn't take the Iranians that long to analyze what is a reasonable deal," he said.

World powers have made a suspension of uranium enrichment a non-negotiable pre-condition for the package, but Annan reiterated Tehran's objections.

"Iran maintains that its interest in nuclear energy is purely for peaceful purposes and I have stressed to Iranian leaders including Mr. Mottaki that it is very much in their interests to convince the world of that by cooperating fully" with the watchdog International Atomic Energy Agency, he said.

"Their point of view is they are coming to the table without preconditions and that everything can be discussed and that I presume includes the question of enrichment."

Annan pointed to the major shift in US policy with Washington now offering to join the talks if enrichment is verifiably suspended.

He added: "I hope that initial shift and signal will bear fruits and as we move forward with the discussions with the Iranians and that sooner or later, rather sooner than later, we'll see the US joining in the talks."

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