Members of the Shiite Hezbollah and the conservative Sunni Al-Ahbash group fought one another with machine guns and rocket-propelled grenades on Tuesday, just blocks from downtown Beirut. Three people, including a Hezbollah official and his aide, were killed, security officials said, in the worst clash in Beirut since May 2008, when Hezbollah gunmen swept through Sunni neighborhoods after the government tried to dismantle the group’s telecommunications network. That fighting brought the country to the brink of a new civil war, but officials insisted that Tuesday’s clash was not the sectarian strife that has bedeviled Lebanon for decades. A joint statement issued later by the two groups said that the episode had stemmed from a “personal dispute and has no political or sectarian background,” and that each side agreed to immediately end their differences and all armed street presences.