BEIRUT, June 12 (Reuters) - Hezbollah is confident that Iran will insist on Lebanon being included in a deal with the United States, a leading Hezbollah politician said on Friday, as hopes grew for an agreement between Tehran and Washington.Hezbollah, founded by Iran's Revolutionary Guards in 1982, entered the regional conflict in support of Tehran on March 2, opening fire at Israel and prompting an Israeli offensive that has killed thousands of people in Lebanon.Iranian officials have repeatedly insisted on an end to fighting in Lebanon as part of any wider agreement."If the agreement happens, we have complete confidence in the Islamic Republic ... we have confidence that it will insist on any agreement including the file of Lebanon," Hassan Fadlallah, a Hezbollah politician, said in an excerpt of a speech broadcast by the group's al-Manar TV.Israeli forces have occupied swathes of southern Lebanon, where Lebanon's National News Agency reported new Israeli airstrikes in several towns and villages on Friday.A Western source said a memorandum between the United States and Iran to halt the war in the Gulf could be signed as soon as Sunday. The source said that language in the memorandum was still being finalised and Iran was sticking to its position that the deal must also end fighting in Lebanon. Last week, Mohsen Rezaei, an adviser to Iran's supreme leader, said Hezbollah had "made great sacrifices" in the war and that Lebanon "will be an inseparable part of any agreement and any ceasefire", in comments reported by the semi-official Mehr news agency.The war in Lebanon has continued despite several ceasefires announced by the United States, which has been mediating talks between the Lebanese and Israeli governments.Hezbollah is not a party to the talks and has demanded the Lebanese government quit the process. Hezbollah rejected a U.S.-backed plan declared last week that would be contingent on the group ceasing fire and withdrawing its fighters from southern Lebanon. (Reporting by Beirut bureau, John Irish in Paris; Writing by Tom Perry; Editing by Aidan Lewis)