Iran live updates: Tehran 'serious' on talks as Trump rejects 'unacceptable' offer

The death toll from Israeli strikes on Lebanon since March 2 rose to 2,846 people as of the Ministry of Public Health's latest update on Sunday, with 8,693 people also reported as wounded.

Sunday's figure showed 51 additional deaths from Israeli strikes since the previous update on Saturday. The continued Israeli attacks come despite a ceasefire agreed by Israeli and Lebanese leaders last month.

Hezbollah -- the Iranian-aligned Lebanese militia -- on Monday claimed fresh attacks on Israeli forces operating in southern Lebanon.

Oil prices climbed after President Donald Trump rejected Iran's latest proposed peace deal as "totally unacceptable," with the U.S. and Iran still appearing far apart on any resolution to the war.

Oil was at nearly $98 a barrel -- up 2.5% -- in U.S. trading as of Monday morning, with global oil at $104, up nearly 3%.

The average price of a gallon of regular gas on Monday was $4.48, down 3.7 cents compared to Sunday and up $1.54 since the war started, according to GasBuddy.

-ABC News' Zunaira Zaki

Iranian Foreign Ministry spokesperson Esmaeil Baghaei told a press conference on Monday that Tehran is "serious" about ongoing negotiations to end the U.S.-Israeli war with Iran, and after President Donald Trump on Sunday dismissed Tehran's latest proposal as "totally unacceptable."

"Diplomatic processes have their own rules, and parties to any negotiation must decide based on their national interests," Baghaei said, as quoted by the semi-official Mehr News Agency.

"The Islamic Republic of Iran has shown it is serious in pursuing its national interests and legitimate rights, while at the same time participating in diplomatic processes with good faith and reason," he added.

Rather, Baghaei said, it is the U.S. that still needs to prove its commitment to a diplomatic process, citing the U.S. withdrawal from the Joint Comprehensive Plan of Action nuclear deal in 2018 and its previous launching of military action despite ongoing talks.

"We fight whenever necessary, and we use the weapon of diplomacy whenever we deem it right," Baghaei said.

The Israel Defense Forces on Sunday conducted strikes throughout the day on several areas in southern Lebanon, which they said targeted Hezbollah infrastructure.

"Throughout the day (Sunday), the IDF struck in several areas in southern Lebanon, more than 20 terror infrastructure, including weapon storage facilities, headquarters, and military used structures from which Hezbollah terrorists operated," the IDF said in a statement.

The strikes come as more talks are scheduled between Israel and Lebanon and Washington later this week.

The Lebanese Ministry of Health released an updated death toll from Israeli strikes, with over 2,800 killed and nearly 8,700 wounded.