Israel will pump gas from the disputed Karish rig with or without an agreement with Lebanon, Prime Minister Yair Lapid's office said in a Monday evening statement.
However, Israel does believe that an agreement to define its maritime border with Lebanon and protect both countries' interests "can and should" be found.
US envoy Amos Hochstein, who is reportedly close to concluding a deal between the Lebanese and Israeli governments to set a maritime border off the Mediterranean Sea, was thanked by Israel for his "hard work in an attempt to bring forth an agreement."
However, the office stressed, gas production will begin as planned and is unrelated to the ongoing negotiations with Lebanon.
Israel unfazed by Hezbollah threats on Karish
On Saturday, Nasrallah said Israel "faces a problem" if it begins to pump gas in a speech given to the Lebanese public. "Lebanon is waiting to receive its demands," he added, referring to the US-brokered deal in the works.
"Lebanon is facing a golden opportunity that may not be repeated to address its crisis," he declared.
Israel prepares to start production at Karish
Finalizing the deal has become increasingly urgent given that the Karish gas field is set to start production next month.
Last week, the Energy Ministry announced it had made progress in preparations to connect the gas field to Israel's nationwide network.
The rig will be tested in the coming days along with its gas transport systems as part of the project's next step, the ministry added.
Lebanese negotiator in New York as deal enters 'final stages'
Lebanon's point-person for the talks to demarcate its maritime border with Israel has arrived in New York, while Lebanese President Michel Aoun says negotiations for a rare deal between the two enemy states have entered their "final stages."
Elias Bou Saab, deputy speaker of Lebanon's parliament, is set to meet with US mediator Amos Hochstein to work out a few remaining disagreements related to the maritime deal, a senior source familiar with the state of negotiations told Reuters.
Aoun wrote on Twitter earlier on Monday that negotiations had reached the "final stages" in a way that guarantees Lebanon's rights to explore for oil and gas.
Reuters contributed to this report.