The ceasefire agreement between Israel and Hezbollah in Lebanon appears to be holding, raising hopes of a lasting respite after a 13-month border conflict that spiraled into an all-out war in September.

Two individuals have been wounded by Israeli fire in southern Lebanon during the second day of a U.S.- and French-brokered ceasefire.

The Israel Defense Forces opened fire Thursday on "suspects" in southern Lebanon who allegedly violated the terms of the ceasefire deal with Hezbollah.

BEIRUT (Reuters) - A ceasefire deal agreed to by Lebanon and Israel expands the area expected to be free of Hezbollah's arms and spells out the Lebanese security forces entitled to carry weapons, sharpening language from prior U.N. resolutions on the matter in ways that appear to corner Hezbollah, diplomats and analysts said.

The truce began Wednesday, bringing a fragile peace to Israel and Lebanon. Israeli troops are to withdraw in phases from southern Lebanon, and Lebanese military convoys headed south to protect the peace.

In a newspaper column, the mayor of Kiryat Shmona, close to the border, said he doubted the ceasefire would be enforced, demanding that Israel creates a buffer zone in south Lebanon. In a poll commissioned by the Israeli station Channel 12 News those questioned were roughly split between supporters and opponents of the ceasefire.

Israel and Lebanon's Hezbollah ceased fire under a deal that aims to end more than a year of hostilities ignited by the Gaza conflict.

Long-displaced residents of south Lebanon have started returning to their homes after a ceasefire between Israel and the Hezbollah militant group took effect early Wednesday morning

United Nations Secretary-General Antonio Guterres said a ceasefire between Israel and Hezbollah in Lebanon that took effect earlier on Wednesday was "the first ray of hope" in the regional conflict after months of escalation.