Mughniyeh, a shadowy figure Israel and the West accused of masterminding terrorist bombings in the 1980s and 1990s, was killed in a car bomb in neighboring Syria in February.
Hezbollah and its supporters regard him as a hero of almost mythical stature. The militant group dubbed Wednesday's prisoner exchange "Operation Radwan" in reference to Mughniyeh's nom de guerre, Hajj Radwan.
"We swear by God ... to continue on your same path and not to retreat until we achieve the same stature that God bestowed on you," said Samir Kantar, who had been the longest-held Lebanese prisoner in Israel.
Kantar had been convicted of a notorious 1979 attack where he allegedly killed a father in front of his 4-year-old daughter, and then killed the girl by crushing her skull with a rifle butt. The girl's 2-year-old sister was accidentally smothered by her mother, who held her hand over the toddler's mouth to stifle her cries while the two hid in a crawl space.
Kantar referred to Mughniyeh's "martyrdom," saying, "This is our great wish. We envy you and we will achieve it, God willing."
A member of the Druse minority sect, Kantar and four Shiite Muslim guerrillas were freed in exchange for the bodies of two Israeli soldiers captured by Hezbollah in 2006. Their capture sparked a 34-day war between Israel and Hezbollah.
Thousands of Israelis mourned at the burials of the two soldiers Thursday.
Later in the day, hundreds of people welcomed Kantar in his hometown of Abey, a mountain hamlet 10 miles south of Beirut.
"This time yesterday, I was in the hands of the enemy (Israelis). But at this moment, I am yearning more than before to confront them," Kantar said.
Israel also returned to Lebanon the bodies of nearly 200 Lebanese and Palestinian fighters who were killed fighting Israel over the past three decades.
Eight tractor-trailers loaded with coffins carrying their remains were driven Thursday from south Lebanon to Beirut. The convoy was stopped often along the way by throngs of supporters in the port cities of Tyre and Sidon, as well as in other towns.
In Sidon, a wooden platform set up as a viewing stand for onlookers as the convoy rolled by collapsed, injuring at least 10 people, including four news photographers, security officials said.
Villagers showered rice and rose petals on the coffins wrapped in Lebanese and Hezbollah flags and covered with wreaths. A banner on one of the trucks read, "The Martyrs of Victory."
Also Thursday, many Lebanese complained they were receiving recorded phone messages from Israel promising "harsh retaliation" to any future Hezbollah attack. The automated messages also warned against allowing Hezbollah to form "a state within a state" in Lebanon. The speaker signs off at the end of the phone messages with the words: "The State of Israel."
There was no immediate confirmation from Israel, though reports surfaced of similar Israeli phone campaigns during the 2006 war.
Israel has never confirmed involvement in such calls, but it is known to use a variety of propaganda and psychological techniques to try to reach Lebanese residents and persuade them not to support Hezbollah.
Lebanon's official National News Agency said residents in south and eastern Lebanon as well as the capital Beirut reporting receiving the calls. It said Telecommunications Minister Jibran Bassil contacted the United Nations to complain, calling it a "flagrant aggression against Lebanese sovereignty."
