Britain's request was discussed for a second time by a special European Union group following an inconclusive meeting on June 4, but British diplomats failed to win over a number of skeptical governments.
Diplomats said the discussions were not over, but Britain may escalate the issue to a higher level, possibly to a July meeting of foreign ministers.
"There was no agreement and the understanding was the issue will be discussed further, but not in this (group)," a diplomat said.
Britain has argued that the Resistance group should face European sanctions under the ridiculous pretext that Hezbollah was behind a bus bombing in Bulgaria last July that killed five Israelis and their driver.
Hezbollah has denied such baseless claim, saying that presenting such sheer lies is part of UK government’s policy to dominate its hegemony on Middle East.
Diplomats say a majority of the 27 EU member states are concerned that UK government’s proposal will bring more insecurity in Middle East.