Over 40 projectiles have been launched from Lebanon across Israel's northern border toward the Galilee and Golan Heights area since Thursday morning, Israeli military officials told ABC News.

Two people were hit by shrapnel and wounded in the Golan Heights, according to Israeli Emergency Services.

The Israel Defense Forces said military exercises are continuing in the north to increase readiness.

-ABC News’ Dana Savir, Jordana Miller, Tom Soufi Burridge and Hugo Leenhardt

Hamas’ new demands in response to the latest cease-fire proposal include an insistence that the timetable be moved up for the withdrawal of Israeli troops from all Gazan territory, according to a U.S. official with knowledge of the negotiations.

The official also said that Hamas communicated additional demands for assurances that a lasting cease-fire would be achieved that were not included in the previous version of the agreement.

In the first days of May, Hamas seemingly accepted a hostage deal presented by Qatar and Egypt, only for Israel to say it had not signed off on that draft, sparking mass confusion. Later, Israel did say it would return to the negotiating table, which eventually led to the formation of the proposal on the table.

-ABC News’ Shannon Crawford

When Hezbollah fired a massive barrage of rockets into northern Israel on Wednesday morning, Meron Bareket said his whole house shook.

"It was kind of a showstopper," Bareket told ABC News. "You just jumped out of your seat."

He lives in Kibbutz Amiad, about 10 miles from the Lebanon border.

Bareket said he quickly ran with his two daughters, ages 2 and 5, to their shelter.

He said he’s fearful the situation on Israel’s northern border "will become a real war."

Bareket said he struggles to explain the situation to his young daughters who have become so accustomed to the sounds and sights of war that they now can differentiate between an F-15 and an F-16 fighter jet when an aircraft flies overhead.

"They point to the sky and ask me if it's safe to go out, and I don't know," he said. "Is it?"

-ABC News' Tom Soufi Burridge, Dana Savir, Tomer Slutzky and Hugo Leenhardt

More than 210 rockets have been fired from Lebanon toward northern Israel since Wednesday morning, the Israel Defense Forces said.

Israeli Prime Minister Benjamin Netanyahu is conducting a security situation assessment Wednesday evening, the prime minister's office said.

-ABC News’ Dana Savir, Bruno Nota and Yael Benaya

All four hostages rescued from Gaza this weekend have been discharged from hospitals, local officials told ABC News.

The three male hostages -- Almog Meir Jan, 22; Andrei Kozlov,27; and Shlomi Ziv, 41 -- were discharged from Sheba Medical Center on Tuesday, according to the medical center.

Noa Argamani, 26, was transferred to Ichilov Medical Center on Saturday to be with her mother, who is in the hospital, officials said. Argamani was discharged on Tuesday morning, a hospital spokeswoman told ABC News.

-ABC News Jordana Miller and Dana Savir