Despite the latest U.S. strikes in Iran, talks toward an initial agreement to end the war continued in Doha on Tuesday, with a high-level Iranian delegation and Qatari mediators meeting in the city and the Trump administration’s negotiators participating from afar, according to two U.S. officials.

Officials and mediators say that Iran and the U.S. are working to reach an agreement on an initial memorandum of understanding that would end the conflict and gradually reopen the Strait of Hormuz while nuclear issues were negotiated.

Although the memo would allow for nuclear negotiations to take place over at least 60 days, the Trump administration still wants to see Iran agree to some big-picture commitments before signing onto the framework, U.S. officials say.

Iran, meanwhile, continues to try to maximize economic incentives to be included in the initial phase of the agreement -- including pushing for the release of frozen Iranian assets, the U.S. officials added.

Another factor is the situation in Lebanon. Iran -- which has insisted Israel's fight against Hezbollah was part of the initial ceasefire deal -- is adamant that the memo should end the conflict there. However, the Trump administration has so far indicated it will continue to back Israel's right to defend itself from Hezbollah.

-ABC News' Shannon K. Kingston

The Israeli military is seizing more territory as it expands ground operations in Lebanon, Prime Minister Benjamin Netanyahu said Tuesday.

"We are deepening our operation in Lebanon. The IDF is operating with large forces on the ground and is seizing controlled areas," Netanyahu said in remarks at the start of a cabinet meeting.

"We are fortifying the security zone to protect the northern communities," Netanyahu added.

-ABC News' Jordana Miller

The internet blackout in Iran has been partially lifted after 87 days of a nationwide blackout.

"Following the mission of the esteemed President and in line with the government's promise, the first step towards free and regulated access to cyberspace has been taken," Mohammad Reza Aref, the first vice president of Iran, said in a statement Tuesday.

Adding, "With the reopening of the internet, smart services will be facilitated, the demands of the people who stood by the system and Iran will be met, and the obstacles to knowledge-based development and scientific authority will be removed."

Israel continues to target Hezbollah infrastructure in southern Lebanon and the Beqqa Valley in the east, saying it hit over 100 sites overnight, the Israeli Defense Forces said Tuesday.

The military issued a warning to residents in the village of Mashghara, in the Beqaa Valley, urging them to evacuate to the north.

A ceasefire between Israel and Lebanon has been in place since mid-April, but Israel has continued to target Hezbollah in several regions.

Hezbollah has continued to target Israeli forces in the southern Lebanon and repeatedly fired projectiles at northern Israel.

-ABC News' Jordana Miller