Israel and Hezbollah traded accusations that their ceasefire had been breached on Thursday, a day after a truce went into effect halting more than a year of fighting in Lebanon.

The Israeli military said the ceasefire, brokered by the United States and France, was violated after what it called suspects, some in vehicles, arrived at several areas in the southern zone.

Hezbollah lawmaker Hassan Fadlallah accused Israel of violating the deal.

"The Israeli enemy is attacking those returning to the border villages," Fadlallah told reporters after a parliamentary session, adding, "there are violations today by Israel, even in this form."

Israeli tank fire hit six areas within that border strip on Thursday morning, striking Markaba, Wazzani and Kfarchouba, Khiyam, Taybe and the agricultural plains around Marjayoun, state media and Lebanese security sources said.

All of the areas lie within two kilometres of the Blue Line demarcating the border between Lebanon and Israel. The buffer zone would be patrolled by Lebanese troops and U.N. peacekeepers. 

One of the security sources said two people were wounded in Markaba.

The Israeli military said in a statement that "several suspects were identified arriving with vehicles to a number of areas in southern Lebanon, breaching the conditions of the ceasefire."

It said troops "opened fire toward them" and would "actively enforce violations of the ceasefire agreement."

Later Thursday, the Israeli military said that its air force struck a facility used by Hezbollah to store mid-range rockets in southern Lebanon, the first such attack since the ceasefire took effect.

Residents told they could return home Wednesday

Lebanese families displaced from their homes near the southern border have tried to return to check on their properties. But Israeli troops remain stationed within Lebanese territory in towns along the border, and Reuters reporters heard surveillance drones flying over parts of southern Lebanon.

There was no immediate comment on the tank rounds from Hezbollah or Israel, who had been fighting for over a year in parallel with the Gaza war.

WATCH | Thousands of displaced people returned to southern Lebanon Wednesday: 

Ceasefire brings some calm to Israel, Lebanon border

A ceasefire between Israel and Hezbollah appears to be holding in Lebanon, bringing some calm to the region, after more than a year of fighting. It’s also allowed thousands of displaced Lebanese civilians to flee for home, despite warnings from the Israeli military to hold off.

The agreement, a rare diplomatic feat in a region racked by conflict, ended the deadliest confrontation between Israel and the Hezbollah militant group in years. But Israel is still fighting the Palestinian militant group Hamas in the Gaza Strip.

Lebanon's speaker of parliament Nabih Berri, the top interlocutor for Lebanon in negotiating the deal, had said on Wednesday that residents could return home.

Israeli forces instructed not to allow residents to return

Under the ceasefire terms, Israeli forces can take up to 60 days to withdraw from southern Lebanon but neither side can launch offensive operations. Israeli Prime Minister Benjamin Netanyahu said he had instructed the military not to allow residents back to villages near the border.

Hezbollah has said its fighters "remain fully equipped to deal with the aspirations and assaults of the Israeli enemy." Its forces will monitor Israel's withdrawal from Lebanon "with their hands on the trigger."

The group has been weakened by casualties and the killing of its leader Sayyed Hassan Nasrallah and other commanders by Israel.

WATCH | Netanyahu facing renewed pressure to end fighting in Gaza:

Israel's PM under renewed pressure to end fighting in Gaza after Lebanon ceasefire

Israel's ceasefire with Hezbollah in Lebanon is leading to a fresh push for Prime Minister Benjamin Netanyahu to reach a ceasefire in Gaza, both from the White House and from Israelis.

More than 3,960 people were killed by Israeli fire in Lebanon during the conflict, many of them civilians, according to the Lebanese Health Ministry. The fighting killed more than 70 people in Israel — more than half of them civilians — as well as dozens of Israeli soldiers fighting in southern Lebanon.

Some 1.2 million people were displaced in Lebanon, and thousands began streaming back to their homes on Wednesday, despite warnings from the Lebanese military and the Israeli army to stay out of certain areas. Some 50,000 people were displaced on the Israeli side, but few have returned and the communities near the northern border are still largely deserted.

Announcing the Lebanon accord on Tuesday, U.S. President Joe Biden said he would now renew his push for a ceasefire agreement in Gaza and urged Israel and Hamas to seize the moment. Months of efforts to negotiate a ceasefire have yielded scant progress, and negotiations are currently on hold.

Israeli military strikes killed at least 21 Palestinians across the Gaza Strip on Thursday, medics said, as forces stepped up their bombardment of central areas and tanks pushed deeper into the north and south of the enclave.