The company said it had terminated an early-stage agreement with the Leviathan partners, led by US oil producer Noble Energy, to take a 25 percent stake worth an estimated US$2.5 billion in the discovery.
Its share price ended 31 cents higher at Aus$41.23 (US$38.06).
Woodside chief executive Peter Coleman said in a statement that negotiations between the parties, which started in late 2012, failed to reach an acceptable outcome on development and supply agreements.
“All parties have worked very hard to secure an outcome which would be commercially acceptable, but after many months of negotiations it is time to acknowledge we will not get there under the current proposal,” he said.
“While Woodside’s commitment to growth is strong, even stronger is our commitment to making disciplined investment decisions.
“I would like to acknowledge and thank the Leviathan Joint Venture participants and the Israeli government for working with us.”
Talks were drawn out as the Israeli government drew up a policy for gas exports. It finally approved the export of up to 40 percent of what it extracts from Leviathan and another field, Tamar, off its Mediterranean coast.
At the time, Israeli Prime Minister Benjamin Netanyahu said the exports would bring in some US$60 billion to state coffers during the next 20 years.
Woodside signed a non-binding memorandum of understanding in February this year outlining its intention to take a stake in the project, running all the downstream gas production operations, with Noble in charge of upstream processing.