BEIRUT, Sept 10 (Reuters) -

Hezbollah's leader said on Tuesday his Iran-backed movement had shot down an Israeli drone in Lebanon for the first time to strengthen deterrence against attack by arch-foe Israel.

On Monday, Hezbollah said it downed and took possession of an Israeli drone in south Lebanon after a flare-up at the border with Israel around a week ago.

The brief exchange of cross-border fire between Hezbollah and Israel marked the fiercest shelling exchange since the long-time enemies fought a deadly month-long war in 2006.

"Despite all the threats and intimidation, today we are affirming the balance of power and reinforcing the deterrent force that protects our country," Hezbollah leader Sayyed Hassan Nasrallah said in a televised speech on Tuesday at a rally marking the Shi'ite Muslim ceremony of Ashura.

He added that there were no longer red lines that Hezbollah would not cross in defending Lebanon from Israeli aggression.

He said this does not mean U.N. Security Council Resolution 1701, which ended the 2006 war, would not be respected, but that Lebanon and its people had the right to self-defense.

The resolution banned all unauthorized weapons between the Litani River in south Lebanon and the U.N.-monitored frontier between Israel and Lebanon.

While the heavily-armed Hezbollah has largely kept its arms out of sight and pledged respect for resolution 1701, it retains a strong presence in the south where it enjoys wide support.

Lebanon's government has long complained to the United Nations about regular Israeli military flights in its airspace in breach of 1701.