The five permanent Security Council members - Russia, China, Britain, France, United States - and Germany have proposed a set of incentives to Iran in a bid to persuade the country to give up its uranium enrichment, which many countries believe is part of a covert weapons program.
"At the moment, Iran should stop its uranium enrichment and accept the proposals of the [Iran] six," Ban Ki-moon said.
Iran, which announced last week that it has launched a second cascade of gas centrifuges to enrich uranium, may face sanctions for failing to comply with the UN Security Council's demand that it suspend enrichment.
The mediators are studying a draft resolution on Iran proposed by Britain, Germany, and France - the so-called EU-3 - that envisions a set of punitive measures against Tehran.
Russia and China, veto-wielding Security Council members with strong business interests in Iran, have consistently opposed sanctions. The two countries have not yet given their formal response to the document, but have insisted on the need for a diplomatic solution.