U.S. Secretary of State said Wednesday that he hopes the latest round of high-level political talks between Israel and Lebanon will result in a joint statement on ending hostilities.

In testimony before lawmakers that started Wednesday shortly after the Israeli and Lebanese ambassadors to the U.S. began meeting at the State Department for a second day of negotiations, Rubio said the aim of the talks is to "produce a joint statement and an action plan on a track for security in that country, independent from Hezbollah, independent from nefarious influence."

A Lebanese official confirmed to Al-Jazeera on Wednesday that Lebanese-Israsli discussions in the Washington round of negotiations are progressing well and that there is "U.S. understanding of the Lebanese approach."

The State Department said progress was made during the first day of talks between Lebanon and Israel in Washington on Tuesday.

"Progress continues on the political and security tracks as we break from the failures of the past 20 years and advance toward a comprehensive agreement aimed at restoring Lebanon’s sovereignty and ensuring Israel's security," the State Department said, adding that "the United States remains fully committed to facilitating these historic negotiations."

Israel warned overnight the Christian neighborhoods in the coastal city of Tyre that Hezbollah members are among them.

Many Lebanese Shiite Muslims fled to those areas in recent days because they were spared from the aerial bombardment along the Mediterranean coast.

President Joseph Aoun condemned Wednesday Iranian attacks on "civilian targets" in Kuwait and Bahrain.

The attack on Kuwait's airport wounded at least 63 people and killed an Indian national.

Lebanese state media reported an Israeli strike near Beirut on Wednesday as well as attacks on south Lebanon, ahead of a second day of talks in Washington between Israel and Lebanon.

The state-run National News Agency (NNA) reported "the targeting of a car on the Khaldeh road", referring to an area at the southern entrance to the capital.

The Lebanese delegation to the Washington peace talks with Israel "sensed Israeli and U.S. acceptance regarding a comprehensive ceasefire, and the three parties presented proposals on specific ceasefire formulas," Baabda sources said on Tuesday.

"There is seriousness and a clear effort and interest from the U.S. in reaching a comprehensive ceasefire," the sources told MTV.

Hezbollah will not accept a "partial ceasefire" with Israel, a senior official from the Iran-backed group said Tuesday, refusing to halt attacks against northern Israel in exchange for Israel sparing Beirut's southern suburbs, although they appeared to have stopped on Tuesday.

Prime Minister Nawaf Salam commented Tuesday on the resumption of Israeli-Lebanese negotiations in Washington by saying that "what remains is to consolidate a ceasefire throughout Lebanon."

The path of negotiation is "the least costly for the country, especially since wars throughout history have ended with a victor and a vanquished, or with negotiations to resolve the conflict," President Joseph Aoun said on Tuesday.