The move came within days of authorities in Thailand claiming they had thwarted a Hezbollah bombing plot in Bangkok, with one of at least two plotters arrested, while Bulgarian security said it found a "suspicious package" in a bus carrying Israeli tourists from Turkey last week.
Both operations followed Israeli warnings of possible bombings by Hezbollah.
Along with Iran, that's Hezbollah's main patron. Tehran and Damascus blamed Israel's Mossad intelligence service for the assassination.
"You killed Imad outside the battleground," Hezbollah leader Hassan Nasrallah warned Israel during Mughniyeh's elaborate funeral.
"Our battle was inside Lebanese territory. You cross the borders. Zionists, if you want open war, let it be open war anywhere."
No one has claimed responsibility for the bombing in the heart of one of Israel's most implacable foes but the Mossad, along with the United States and France, had hunted Mughniyeh since the 1980s.
The Mossad, and the military's crack Special Forces unit, Sayeret Matkal, have made "targeted assassinations" their specialty over the last three decades and Mughniyeh's assassination in Damascus bore the hallmarks of an Israeli operation.
So did last week's broad-daylight assassination of an Iranian nuclear scientist in Tehran. He was the fourth scientist killed there in the last two years in what is widely seen as an Israeli campaign to slow down Iran's contentious nuclear program.
That killing, amid an escalating confrontation in the Persian Gulf between the United States and Iran, has antagonized Tehran, Hezbollah's ideological master, against Israel and could, some analysts suspect, substantially heighten the prospect of a Hezbollah attack on Israelis.
"Hezbollah, a creature of the Iranian Islamic Revolution, has a long history of receiving aid from Iranian embassies in its overseas operations," the U.S. global security consultancy Stratfor observed recently.
Ashkenazi, who was the chief of Israel's general staff at the time of the Mughniyeh slaying, retired from the military in February 2011. At that time he was under round-the-clock protection because he had been targeted in a Hezbollah plot uncovered in August 2009.
An Israeli Arab named Rawi Sultani was arrested by Israel's internal security service, on charges of planning to kill Ashkenazi in a plot supposedly masterminded by Hezbollah.
The charges were reduced after Sultani agreed to cooperate with authorities. On April 6, 2010, a Tel Aviv court sentenced him to six years in prison for giving Hezbollah information on Ashkenazi.
Sultani, a member of a prominent Arab family, was a member of the Kfar Saba Country Club outside Tel Aviv where Ashkenazi regularly worked out at the state-of-the-art gym. That was where the Israeli general was to have been killed.
Sultani, then 23, confessed he had been contacted by a Hezbollah operative in 2008 during an Arab youth summer camp in Morocco.
The plot targeting Ashkenazi is seen by Israeli security authorities as one of as many as 10 attempts by Hezbollah against the Jewish state to avenge the slaying of Mughniyeh.
Apart from the plot against Ashkenazi, all of the attempted strikes were planned to take place outside of Israel where its citizens are more vulnerable. These include a 2008 plot to blow up the Israeli Embassy in Baku, Azerbaijan, a former Soviet republic that is Iran's uneasy northern neighbor.
Israeli intelligence has been making major inroads in Azerbaijan in recent years, much to Tehran's dismay, as part of its global shadow war with the Islamic Republic that stretches from Latin America to Central Asia.
Two Lebanese, identified by Azeri authorities as members of Hezbollah and reportedly working with Iran's intelligence apparatus, were arrested with four Azeris. The Lebanese were sentenced to 15 years in prison, but, along with 12 Iranians, were reportedly released in August 2010 as part of a prisoner exchange between Azerbaijan and Iran.
Other apparent Hezbollah revenge attacks were reportedly foiled in the Netherlands, Turkey and elsewhere.