BEIRUT (Reuters) - Lebanon's army chief told his soldiers on Tuesday to be extra vigilant to prevent unrest during political turmoil after the prime minister quit, and accused Israel of "aggressive" intentions at the southern frontier.

Troops should be ready to "thwart any attempt to exploit the current circumstances for stirring strife," the army's Twitter account quoted General Joseph Aoun as saying ahead of Independence Day celebrations on Wednesday. "The exceptional political situation that Lebanon is going through requires you to exercise the highest levels of awareness."

Aoun called on troops to "assume full readiness at the southern border to face the threats of the Israeli enemy, its violations, and the aggressive intentions it is indicating towards Lebanon."

A senior Israeli official dismissed the warnings of border aggression as "nonsense".

Lebanon was thrust back onto the forefront of regional rivalry between Sunni Saudi Arabia and Shi'ite Iran, after its prime minister quit this month in a broadcast from Riyadh.

In his shock resignation, Saad al-Hariri railed against the Iran-backed Shi'ite military and political movement Hezbollah, which both Saudi Arabia and Israel consider an enemy. The Lebanese president has refused to accept Hariri's resignation until he returns to Lebanon.

The Saudis have demanded that Hezbollah stop meddling in regional conflicts and say it must disarm. Hezbollah has long said it must keep its arsenal to protect Lebanon from Israel, and its leader Sayyed Hassan Nasrallah accused the Saudis this month of inciting Israel to attack Lebanon.

He said he could not rule out a new clash with Israel, although he described it as unlikely. In a televised speech on Monday, Nasrallah suggested the Saudis and Israelis were working together.

Tensions grew earlier this year between Israel and Hezbollah, which fought a month-long war in 2006 that killed around 1,200 people in Lebanon, mostly civilians, and 160 Israelis, most of them troops.

Israeli Energy Minister Yuval Steinmetz said this week that Israel has had covert contacts with Riyadh amid common concerns over Iran, a rare disclosure by a senior official from either country of long-rumored secret dealings.

"ALL OUR MIGHT"

But Israel dismissed claims that it is planning military action against Hezbollah at the behest of Saudi Arabia.

"We are not interested in an escalation with Lebanon," Israeli Education Minister Naftali Bennett, a member of the security cabinet, told Reuters about the accusation of Israeli-Saudi collusion.

However, Bennett added: "If rockets are fired from Lebanon at Israeli cities, then we will see that as a declaration of war by the state of Lebanon and will act with all our might."

In Israel, where the 2006 war was widely seen as inconclusive, there is little in the public mood or political discourse to suggest fighting with Hezbollah is imminent. But Israeli officials have voiced deep concern about Iran and Hezbollah's expanding influence in the region.

"The Saudis and Israel definitely have common interests today," including the threat from Iran, Israeli Justice Minister Ayelet Shaked said in a radio interview last week. "The countries' coming together could serve both of them."

But, Shaked said, "we don't work for anyone. We first and foremost look out for our interests."

(Reporting by Ellen Francis; Additional reporting by Maayan Lubell and Jeffrey Heller in Jerusalem; Editing by Peter Graff)