Miller-Heidke, who performed atop a moving pole in a billowing white gown, sang Zero Gravity, a ballad about emerging from depression, for the crowds in Israel.
"We know that at a certain stage there was an attempt, apparently by Hamas, to commandeer our digital broadcast", chief executive, Eldad Koblenz, told Israel's Army Radio.
Some pro-Palestinian activists have called for performers and worldwide broadcasters to boycott the show due to Israel being the host nation.
A missile fired from Israel's Iron Dome air defence system, created to intercept short-range rockets.
The Sabbath was said to be one of the reasons Eurovision organisers and Israeli hosts decided against holding the event in the religiously conservative city of Jerusalem.
Palestinians and their foreign supporters have called on, so far fruitlessly, countries to shun the Tel Aviv songfest as part of wider efforts to isolate Israel internationally. Last year's victor was Israeli entrant Netta Barzilai with the song "Toy", which went on to top the Billboard dance club chart in the USA in August, a first for an Israeli singer.
Semi-final rounds are slated for Tuesday and Thursday, followed by the finals on Saturday evening.
"I'll never stop playing music to suit someone's political agenda", Madonna said in her statement to CNN, "nor will I stop speaking out against violations of human rights wherever in the world they may be".
On Tuesday, hundreds of protesters marched in Tel Aviv before the first semi-finals.
Sand did not say what issues were delaying the signing of a contract, but confirmed that negotiations were in a "final stage".
He is facing a May 29 deadline to form a new government.
Israel's government has tried to clamp down on opposition by launching a PR campaign using Google Ads which refers to the words "boycott" and "Eurovision", but leads to a glossy website extolling Israel as "Beautiful, Diverse, Sensational" - in a play on the BDS initials for the Boycott, Divestment, Sanctions (BDS) movement. Just like South Africa, time to boycott apartheid.
Demonstrators have vowed to continue their protests throughout the week's event.
Later in the song, she sings: "Israel's been flouting global law, and human rights lie trampled on the floor".