Fifteen years later, it is starting to view him in a slightly different light and Israeli analysts say he might yet prove the man who can open a dialogue between Hamas and Israel.
Mashaal is due to make his first visit to the Gaza Strip on Friday for a two-day stay to join celebrations for Hamas' 25th anniversary and to take part in what the militant group says will be a victory rally after its recent conflict with Israel.
Israeli leaders have an alternative view of the eight-day conflagration, which ended in a ceasefire. They say they dealt Hamas a sharp blow which should deter rocket fire out of the small coastal territory for many months to come.
They also believe the fighting distanced Hamas further from Shiite Iran's sphere of influence and put it squarely in the camp of Sunni Muslim powers Qatar and Egypt -- with Mashaal, who has lived in exile from his native West Bank for 45 of his 56 years, the key player in this evolving regional shift.
"From Israel's point of view, Khalid Mashaal now plays a more positive role," said Shlomo Brom, a senior research fellow at the Institute for National Security Studies, an independent research institute based in Tel Aviv.
"Generally speaking, Hamas is divided into two factions, the Gaza faction and the external faction. There is a debate between them on several levels, and Mashaal's external faction is much more moderate. This is why he is of interest to Israel."
No cabinet minister in Israel would call Mashaal a moderate, at least not in public. To Israelis, Hamas is synonymous with suicide bombings and rocket fire. It is classed by Israel and its Western allies as a terrorist group and widely condemned for refusing to renounce violence and recognize Israel.
But in recent years Meshaal has adopted a more nuanced stance, backing the idea of a long-term truce in return for a withdrawal to the lines established ahead of the 1967 war, when Israel seized East Jerusalem, the West Bank and Gaza Strip.
"We accepted it, but not at the expense of recognizing Israel or giving away Palestinian rights, but as a common (Arab) factor," he told Reuters last week in Qatar, where he has lived since quitting Syria some months ago.Exiting the axis
Mashaal's decision to leave Damascus after falling out with President Bashar Assad over his crackdown the countrywide uprising, was greeted with secret glee in Israel.
The Hamas leader himself told Reuters that the move affected ties with the group's main paymaster and weapons' supplier, Iran -- a country Israel believes is by far the greatest threat to it, because of its ambitious nuclear program.
"Hamas' external leadership is trying to leave the Iranian axis. This is remarkable, but it won't be easy because they are still dependent on Iranian arms," said INSS research fellow Yoel Guzansky. "In the end, it could be good for Israel."
The abrupt departure from Syria initially weakened Mashaal within Hamas. His relations with Damascus and Tehran had made him an essential linchpin, but with those links damaged or broken, the Gaza leaders started to assert their authority.
Hamas's internal dynamics are shrouded in secrecy, but those in Gaza have enjoyed more influence since they managed to seize control of the isolated enclave in 2007 after fighting with the allies of President Mahmoud Abbas. He exercises only limited Palestinian self-government in the Israeli-occupied West Bank.
A senior Israeli official, who declined to be named, said he was not convinced that Mashaal had done enough to restore his credibility within Hamas as undisputed leader. "There is a power struggle going on," he said. "But they are keeping it hidden."
Adopting Prime Minister Benjamin Netanyahu's uncompromising line, the official also dismissed suggestions that Mashaal might one day be willing to sit down and talk with Israel.
"Between the various leaders, there are small differences between what they say, but at the end of the day, it is all shades of black," he said. "They all lead a terror group."
Netanyahu played an accidental but important role in establishing Mashaal's militant credentials when he ordered Mossad agents to kill him in 1997 in retaliation for a Jerusalem market bombing that killed 16 people and was blamed on Hamas.
The agents were caught by Jordanian police after injecting Mashaal with poison in the street; Netanyahu, in his first term as premier, was forced to hand over the antidote and the incident turned the middle-aged former schoolteacher into a hero of the Palestinian resistance.
"In a movement like Hamas, being the target of a political assassination is a medal of honor, and he wore that medal on his chest," said Itamar Rabinovich, a former Israeli ambassador to the United States who teaches at Tel Aviv University.Changing dynamics
Israel has long regarded Hamas as a dangerous, yet containable menace. At one time the group dispatched suicide bombers into Israeli cities. Then it attacked from Gaza, firing thousands of rockets at Israel's southern borderlands.
Successive Israeli governments have hit back at the Gaza Strip. In 2008-2009, Israel launched a three-week offensive that killed 1,400 Palestinians while 13 Israelis died. In November, it waged an eight-day battle, which left over 170 Palestinians and six Israelis dead.
Unlike four years ago, Hamas had more to cheer about at the end of the last round of fighting.
For the first time, its missiles managed to reach the Tel Aviv and Jerusalem areas. It also showed the world that it had the solid backing of top Arab nations - most notably Egypt - whose support appeared at best lukewarm before the Arab Spring.
These changing regional dynamics undoubtedly stayed Israel's hand. Unlike in 2009, it did not launch a ground offensive although thousands of troops with tanks were massed on the border ready to move in. And it swiftly accepted Egyptian mediation, unwilling perhaps to do anything that might irreparably damage cherished diplomatic ties with Cairo.
The three sides are now engaged in talks in Egypt aimed at strengthening the ceasefire. Hamas demands an end to the land and sea blockade imposed in 2006, which is aimed at halting the import of arms into Gaza and which has stifled economic growth.
In 2010, under international pressure to relax its blockade, Israel rolled back some of the controls on imports and exports via its land links, and more concessions are now likely, officials say. However, the sea blockade looks certain to remain in place as long as Hamas demands the right to rearm.
The fact that talks are taking place, albeit via mediators, shows that Israel and Hamas are already engaged in a dialogue. Israeli analysts say this could deepen if Mashaal can predominate in Hamas and develop a more tempered discourse.
No one expects such talks, if they ever happen, to bring about the end of the decades-old Middle East conflict, but they might at least ensure that it does not degenerate further.
"Officially we say we are not dealing with them, but things are changing before our eyes," said Uzi Rabi, director of the Moshe Dayan Center for Middle Eastern Studies in Tel Aviv.
"If Khalid Mashaal can deliver, believe you me, someone here will talk to him, even behind the scenes."
JERUSALEM (Reuters) -- Israel once tried to kill Hamas leader Khalid Mashaal in a botched assassination attempt on the streets of the Jordanian capital, Amman.