BEIRUT, Nov 21 (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 across the southern frontier.

Troops should be ready to "thwart any attempt to exploit the current circumstances for stirring strife...and chaos," the army's Twitter account quoted General Joseph Aoun as saying.

"The exceptional political situation that Lebanon is going through requires you to exercise the highest levels of awareness and vigilance," he said ahead of Independence Day celebrations on Wednesday.

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".

Shi'ite movement Hezbollah's heavily armed militia is at the heart of Lebanon's political crisis, part of a regional struggle between Sunni Saudi Arabia and Shi'ite Iran. Lebanon's governing system maintains a balance between Sunni, Shi'ite, Christian and Druze factions that fought a 1975-1990 civil war.

Prime Minister Saad Hariri resigned on Nov 4 in a broadcast from Saudi Arabia, railing against Iran and its Lebanese ally Hezbollah. A long-time Saudi ally and Sunni leader, Hariri has yet to come back to Beirut.

President Michel Aoun, a Christian leader and Hezbollah ally, refuses to accept Hariri's resignation until he returns. In the meantime, Hariri left Paris for Egypt.

The Saudis have demanded that Hezbollah stop meddling in regional conflicts to resolve the crisis, and say it should disarm. Hezbollah has long said it must maintain its arsenal to deter Israel from attacking Lebanon.

Tensions grew earlier this year between Israel and Hezbollah, which have avoided a major conflict since fighting a month-long war in 2006 that killed around 1,200 people in Lebanon.

Aoun said troops should uphold a U.N. Security Council resolution that ended the 2006 war, which gave the Lebanese military sole responsibility for guarding its side of the border. The United Nations maintains a peacekeeping force there.

In a televised speech on Monday, Hezbollah leader Hassan Nasrallah suggested the Saudis and Israelis were working together. Nasrallah also accused Riyadh this month of inciting Israel to attack Lebanon.

An Israeli cabinet minister 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