The Western powers are hoping to persuade Iran to freeze its uranium enrichment programme, but are threatening new sanctions if it fails to do so.
Russia has also indicated that it may support new sanctions.
Low-enriched uranium can be used as fuel for power plants while highly enriched uranium can be used to make nuclear bombs.
Earlier Israeli Foreign Minister Avigdor Lieberman said the disclosure proved Iran wanted to equip itself with nuclear weapons" and that Israel wanted to see an "unequivocal" Western response to the development.
Iranian atomic energy chief Ali Akbar Salehi said on Saturday that inspectors from the International Atomic Energy Agency (IAEA) could visit the new site under Non-Proliferation Treaty rules.
Mrs Clinton said after meeting foreign ministers from Gulf countries: "It is always welcome when Iran makes a decision to comply with the international rules and regulations, and particularly with respect to the IAEA.
"We are very hopeful that, in preparing for the meeting on October 1, Iran comes and shares with all of us what they are willing to do and give us a timetable on which they are willing to proceed."
Western powers have been urging Iran to allow access to the site
The secretary of state's remarks came hours after President Barack Obama said he remained open to "serious, meaningful dialogue" with Iran to resolve the issue.
Failure to comply with inspectors could lead to tough international sanctions, he said.
On Friday, President Obama, French President Nicolas Sarkozy and British Prime Minister Gordon Brown demanded that Iran allow UN inspectors into the second site.
Iran's President Mahmoud Ahmadinejad said on Friday that Tehran had conformed to IAEA rules, by informing the agency about the site a year earlier than it needed to.
But BBC world affairs correspondent Paul Reynolds says there is a dispute about the amount of notice that Iran is required to give the IAEA before a new nuclear facility becomes operational.
In 2003, Iran agreed on what is called a Subsidiary Arrangement, under which it is required to tell the IAEA at the preliminary design stage.
Iran later announced that it had repudiated this agreement, but the IAEA says that no unilateral repudiation is allowed.
On Saturday, the chief of staff for Iranian Supreme Leader Ayatollah Ali Khamenei said the second enrichment plant would "become operational soon".
Meanwhile Iranian media reported that the elite Revolutionary Guards would start missile defence exercises on Sunday, in a move which seems guaranteed to increase tensions further.
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