The London Palestinian Action is part of Boycott, Divestment, Sanctions (BDS) - a Palestinian-led movement for freedom, justice and equality, according to a dedicated web site. "I hope and pray that we will soon break free from this awful cycle of destruction and create a new path towards peace", she said.
"We are in a situation now that is a bit odd", said Eurovision's executive supervisor, Jon Ola Sand, at a news conference in Tel Aviv. The news comes despite the music legend's scheduled arrival in Tel Aviv on Wednesday morning aboard the private jet of Israeli-Canadian billionaire Sylvan Adams.
The Israeli authorities have confirmed that they were taking unprecedented security measures to provide security and safety in Israeli towns in general, particularly in the Tel Aviv area and the center, with the holding of the Eurovision song contest.
Seventeen global acts will take to the stage but only 10 will make it to the 26-strong grand final on Saturday May 18.
Oddie said that the band's boycott of Eurovision was in response to "a call from Palestinian civil society".
"We are negotiating now, in the final stage of that - but if there is no signed contract this week, she will not be on the stage".
However, while fans of the Medellin singer had thought it was a done deal, Eurovision's executive supervisor Jon Ola Sand has thrown things into doubt.
"We have an artist who would like to participate in the Eurovision Song Contest, and who we would love to welcome on that stage".
Her latest rendition, which has been updated since Australia's first televised decider, saw Miller-Heidke and two dancers sway metres above the stage.
The start of the contest was marked with a protest by pro-Palestinian activists, calling to put an end to Israel's control of the West Bank and Gaza policies, who marched near the show's venue in Tel Aviv.
The European song contest kicked off in the Israeli capital Tel Aviv on Tuesday amid the reported deployment of the country's Iron Dome anti-rocket systems.
The UK, as one of the "big five" countries, along with France, Germany, Italy and Spain, are already assured of a place in the grand final.
Israel has won the Eurovision Song Contest four times, hosting twice in Jerusalem in 1979 and 1999.
The live show is watched by about 200 million viewers worldwide.