The EU's "big three" are said to have backed down from a demand that the UN nuclear watchdog should immediately report Iran to the Security Council.
Iran resumed uranium conversion work in August
Diplomats from France, the UK and Germany said the shift came amid opposition from Russia and China.
They are now reportedly proposing that the International Atomic Energy Agency (IAEA) in Vienna should only implicitly threaten Tehran with such action.
Iran is accused of developing atomic weapons, an allegation it denies.
The secretary of Iran's Supreme National Security Council, Ali Aghamohammadi, told the BBC that the decision by Europe not to refer Tehran could decrease tension.
The BBC's Tim Franks at the Vienna talks says that in effect Tehran would be given until the end of October to allow the IAEA all the access it demanded to Iran's nuclear plants and officials.
The Islamic republic insists its nuclear activities have not violated the nuclear Non-Proliferation Treaty.
It has warned that if referred to the Security Council, it could start uranium enrichment - a possible step toward making nuclear arms - and stop allowing unfettered IAEA inspections of its nuclear facilities and programmes.
The IAEA board of governors is meeting this week at the agency's headquarters in Vienna.
At least a dozen of the 35 member states opposed the original EU draft resolution - backed by the US, a stern critic of Tehran - that called for immediate referral to the UN Security Council, a move that could trigger sanctions.
According to the Associated Press news agency, the new draft now says only that suspicions over Iran's nuclear programme are "within the competence of the Security Council".
It accuses Iran of "excessive concealment, misleading information and delays" in giving IAEA officials access to nuclear materials.
It also expresses serious concern that Iran has failed to "re-establish full suspension of all enrichment-related activities", a reference to last month's resumption by Tehran of uranium conversion.
Conversion is a prelude to enrichment - a key step in the manufacture of nuclear arms.
The US appears to be behind the revised resolution.
"Our goal is to build the broadest possible consensus," State Department spokesman Adam Ereli said.
The threat of referral was not being withdrawn, he told reporters, adding it was "a question of not if, but when" the issue would go before the Security Council.