Iranian officials made the "extraordinary" demand during talks in Paris on defusing international tension over Tehran's nuclear intentions, the newspaper's diplomatic editor reported.
During the meeting, which the Daily Telegraph said took place earlier this month, the Europeans tried to convince their Iranian counterparts to honour an earlier deal to suspend a controversial uranium enrichment programme.
Instead the Iranians set out their own demands, stating that Europe's three biggest nations -- two of them nuclear powers -- should back Iran's quest for "advanced (nuclear) technology, including those of dual use".
Britain, France and Germany, they said, should "remove impediments" preventing Iran from having such technology, and do so regardless of any "legal (or) political... limitations," an apparent reference to US pressure or international sanctions, the newspaper said.
Furthermore, the Iranian side stated that London, Paris and Berlin should agree to meet Iran's requirements for conventional weapons, and to "provide security assurances" against a nuclear attack on Iran, it said.
The latter was an apparent reference to Israel's nuclear firepower, which includes long-range missiles, the Daily Telegraph said.
While Britain, France and Germany are still debating how to respond to the demands, the newspaper quoted British officials as calling them "extremely surprising, given the delicate state of process".
It added that, according to the British officials, Iran's demands had "gone down very badly".
Officials from Britain, France and Germany met with an Iranian delegation in the French capital in the last week of July, but European Union diplomats revealed nothing afterwards about Iranian demands such as reported in the Daily Telegraph.
Rather, they said the talks had produced "no substantial progress" as each side repeated their positions. "There were no changes," one diplomat told AFP in Tehran on August 1.
Under an agreement reached last year with the three European powers, Iran agreed to suspend sensitive uranium enrichment, allow tougher inspections and file a comprehensive declaration of its nuclear activities.
Those measures were aimed at "building confidence" while the International Atomic Energy Agency (IAEA) conducted a major probe into Iran's bid to generate electricity through nuclear power -- seen by the United States as a cover for secret weapons development.
But since then, experts from the UN's nuclear watchdog have found omissions in Iran's reporting. Inspection visits have also been delayed, and Tehran has backed away from a pledge to suspend all enrichment-related activities.