An Israeli newspaper, Maarif, reported on Sunday that the statements came after several European countries which have been putting pressure on Israel to stop its violation of Lebanese air space.
Israel claims it has to carry on monitoring Lebanon from the air to prevent possible arms-smuggling to Hezbollah.
Amir Peretz, the defence minister, was said to have told the weekly cabinet meeting: "The Lebanese government is falling short of carrying out its commitment under UN Security Council Resolution 1701."
The resolution ended the 34-day war between Israel and Hezbollah.
"Increasing intelligence indicates a growing effort to pass weapons into Lebanon," he said.
"As long as these attempts continue, the legitimacy of our flights over Lebanon increases, as long as (UN) Resolution 1701 is not carried out, we have no intention of stopping the flights over Lebanon."
Israel has continued to carry out flights over Lebanese territory despite a UN-brokered ceasefire since August 14.
The flights have been increasingly criticised, with France - which currently heads the UN peacekeepers in Lebanon - speaking out last Friday against the violations.
Michele Alliot-Marie, the French defence minister, told reporters at United Nations headquarters at the time: "These violations are extremely dangerous because they may be felt as hostile by forces of the coalition that could be brought to retaliate in case of self-defence and it would be a very serious incident."
UN Resolution 1701 called for the disarming of all militias in Lebanon, the withdrawal of Israeli troops from the south of the country, and the deployment of a beefed-up UN peacekeeping force.
Peretz said on Sunday that the purpose of the United Nations Interim Force in Lebanon (Unifil), was to act against Hezbollah and not Israel.
"Unifil is meant to act against Hezbollah and not against Israel. Israel's security is the most important objective"
"Unifil is meant to act against Hezbollah and not against Israel," he said. "Israel's security is the most important objective."
On July 27, Israeli warplanes bombed a UN observation centre in southern Lebanon and killed four observers.
Unifil was created by the security council in 1978 to confirm Israeli withdrawal from Lebanon. Following the July/August 2006 crisis, the council enhanced the force and decided that, in addition to the original mandate, it would, among other things, monitor the cessation of hostilities. It would also accompany and support the Lebanese armed forces as they deployed throughout the south of Lebanon.
Israel has been involved in southern Lebanon since the Arab-Israeli wars in 1948 and 1967 when Palestinian refugees took refuge in Lebanon.
Israel launched its war on July 12 after Hezbollah seized two soldiers and killed eight others in cross-border raids.
The war killed more than 1,200 Lebanese, mostly civilians, and more than 160 Israelis, mostly soldiers.