Answer:
The Islamist militant group based in Lebanon and supported by Iran that is being closely monitored for its involvement in the ongoing conflict between Israel and Hamas is Hezbollah. Hezbollah is a Shia Islamist political and military organization that emerged in the 1980s during the Lebanese civil war. It has since evolved into a powerful force in Lebanese politics and maintains a significant armed wing.
Hezbollah has been involved in various conflicts and has a history of engaging in armed resistance against Israel. It fought against Israeli forces during the Israeli occupation of southern Lebanon, which lasted from 1982 to 2000. It has also been accused of carrying out attacks against Israeli targets abroad.
In the context of the ongoing conflict between Israel and Hamas, Hezbollah's support for Hamas is primarily through ideological and political solidarity. While Hezbollah has not been directly involved in the recent hostilities between Israel and Hamas in Gaza, it has expressed support for Hamas and condemned Israeli actions. The group's close ties with Iran, which is a major supporter of Hamas, contribute to its monitoring in relation to the conflict.