A British foreign office spokesman said: "We will be disappointed if there (is) no response to the E3 proposals by [Tuesday].
"We will have no choice but to ask the UN to proceed with further sanctions."
The French foreign ministry echoed that stance, saying Iran "will have to face new sanctions" if it does not respond positively by Tuesday to the "sanctions freeze-for-enrichment freeze" offer.
Paris "expressed its disappointment at the lack of a clear response from Iran" to the proposals, the ministry said in a statement.
In New York Jean-Pierre Lacroix, France's deputy UN ambassador, told the AFP news agency: "If we don't get an encouraging response from the Iranians, we will have to show firmness, resort to sanctions as in the past."
Javier Solana, the EU foreign policy chief, earlier held what a spokesman described as "inconclusive" talks with Saeed Jalili, Iran's chief nuclear negotiator, after Tehran missed a deadline set by Washington to respond to the proposed trade and economic incentives.
Gonzago Gallegos, a US state department spokesman, said Jalili told Solana that Tehran would provide a written response on Tuesday.
Iranian state-run television reported that in the Solana-Jalili telephone conversation, "both sides agreed to continue talks", and Solana's spokesman said that further contacts between the EU and Iran "are not ruled out in the coming days".
The TV channel said: "They also emphasised that preserving this path (talks) needs a positive and constructive atmosphere."
For their part, senior diplomats from the US, Britain, France, Germany, Russia and China discussed the latest developments by telephone on Monday and agreed to push for new action against Iran if it continued holding out.
Tehran has steadfastly refused to suspend its uranium-enrichment activities, which it says are aimed only at producing fuel for nuclear power production.
The Western powers fear the programme is a cover for developing nuclear weapons.