(Adds statement by Olmert's office)
JERUSALEM, Feb 14 (Reuters) - Israel put its embassies and other interests abroad on high alert and reinforced troops on the Lebanese border on Thursday after the assassination of Hezbollah's top guerrilla commander.
Hezbollah's chief Sayyed Hassan Nasrallah threatened Israel with "open war" after the Shi'ite Muslim group and its main backer Iran accused the Jewish state of killing Imad Moughniyeh with a car bomb in Damascus on Tuesday.
The Israeli government rejected the charge, although its Mossad spy service had long regarded Moughniyah as a "terrorist mastermind".
Prime Minister Ehud Olmert's office advised Israelis that the Counter-Terrorism Authority, which issues travel warnings, recommended Israelis overseas avoid congregating in large groups and cautioned they could be targets of kidnapping attempts.
"Hezbollah has yet again accused Israel of killing Imad Moughniyah, which points to an increased threat of terror attacks by Hezbollah against Israeli targets abroad," Olmert's office said in a statement.
With supporters of the Shi'ite Lebanese militia urging revenge, Israel stepped up already stringent security measures.
"Our diplomatic missions are on high alert, and this could be the case for weeks or even months -- it depends on our risk assessments," a security source said. "There have also been precautions taken in terms of our (Lebanese) border garrison."
Moughniyah, who had also topped U.S. wanted lists, was the most senior member of Hezbollah to be killed since its previous secretary-general, Abbas Mussawi, was killed in a 1992 Israeli helicopter ambush in southern Lebanon.
That killing was followed closely by the bombing of the Israeli embassy and a Jewish community centre in Argentina, attacks that claimed dozens of lives and which Israel described as the work of Iranian agents. Tehran denied involvement.
"To my regret, we are aware of the past in this context, and we know how to prepare for further scenarios," Internal Security Minister Avi Dichter told Israel Radio.
Citing a U.S. statement welcoming Moughniyah's death, Dichter added: "The world is cleaner now that he has left us."
In an earlier statement, Olmert's office departed from a policy of not commenting on intelligence operations abroad and said it rejected the "attempts of terror elements to attribute to Israel any involvement in this incident".
A senior Israeli government source said the aim was containment, to avoid a new confrontation.
Experts were divided on how quickly Hezbollah might try to avenge Moughniyah's death by striking Israel, given the vigilant standoff between the sides since their 2006 war in Lebanon.
"Retaliation will mean a change in the ground rules in confrontation with Israel," a Lebanese political source said. "Such a decision needs to be taken with a cold head so there would be no rush to respond."
Israeli pundits appeared mostly convinced Mossad had a hand in Moughniyah's killing, not least because the tactics recalled the assassination of a leader of the Palestinian Islamist militant group Hamas in the Syrian capital in 2004.
Some Israelis said Moughniyah's value as a military target could be outweighed by the danger of future Hezbollah reprisals.
"Is all this worth Hezbollah's revenge, in the form of a terrorist attack abroad or something else?" commentator Ofer Shelah wrote in Israel's Maariv newspaper.
But Amnon Lipkin-Shahak, a former chief of Israel's armed forces, described such thinking as largely irrelevant. (Additional reporting by Nadim Ladki in Beirut)
Our Standards: The Thomson Reuters Trust Principles.