Two weeks’ vacation in Italy is a great way for a foreign-affairs columnist to escape from regular duty. As I left Rome on Thursday, Prime Minister Silvio Berlusconi was entertaining Libyan leader Moammar Gadhafi, who arrived with a group of female bodyguards and pitched his bedouin tent in a public park.

In the meantime, Berlusconi’s wife was accusing him of dallying with an 18-year-old, and a court was investigating whether he used government planes to shuttle guests to parties at his Sardinian villa. But voters still gave his coalition a plurality last week in elections for the European parliament.

After such opera bouffe, it’s a bit hard to get back to serious international matters, like President Obama’s seminal speech to the Muslim world on June 4 in Cairo. But let me try.

Some critics have derided Obama’s speech as naive for pitching a new beginning between the United States and the world’s Muslims. Some say he raised expectations about the Arab-Israeli peace process that he can’t deliver on, or that he gave short shrift to promoting democracy or women’s rights in Muslim countries.

They are missing the point (although one can find fault with specific passages). This speech won’t suddenly transform our relations with Islamic countries. Yet, it laid the ground for a shift in Muslim opinion about America, especially among young people, that could undercut the appeal of militancy.

The impact of that shift can already be seen in Pakistan, and in last week’s elections in Lebanon and Iran.

How so? The Bush administration’s blanket equation of terrorism with Islam helped stoke popular support for radical Islamists. So did the Bush team’s botched handling of the Iraq war and postwar Afghanistan, and its decision to leave the Israeli-Palestinian peace process on ice.

Bush was perceived in the region as hostile to Muslims and Arabs. He openly promoted democracy and tried to impose it in Iraq, but the bloody chaos in Baghdad gave democracy a bad odor. Arab democrats became wary of any association with U.S. financing or support.

In the Arab world and Pakistan, Osama bin Laden could gain traction with videotapes that denounced America’s “hatred” of Muslims. Radical Islamic Web sites played on the same message. In Iran, President Mahmoud Ahmadinejad could rally Persian nationalists by claiming that imperialist America wanted to attack their country.

Obama’s speech undercut those images so valuable to radicals. In fact, a new bin Laden audiotape, broadcast on June 4 condemning Obama, fell flat.

Contrary to critics, Obama did not pull any punches about his determination to fight violent extremists, including the Taliban and al-Qaeda. He firmly debunked the myth – still circulating in the Muslim world – that 9/11 didn’t happen or had some justification. He explained why we continue to fight in Afghanistan (and stressed that we don’t want to keep troops there).

However, he couched that battle in far different language than the Bush administration. He stressed that we are “not at war with Islam.” He did not use the words terrorist or Islamofacism. But he emphasized that the militants threaten, and have killed, Muslims.

There was no applause when he talked of the need to isolate extremists in Muslim communities. But there was applause at one crucial passage: when he said the militants’ actions were not reconcilable with Islam. “The Holy Koran teaches that whoever kills an innocent is as if he has killed all mankind,” Obama said. And the audience clapped.

The reason such words are so important can already be seen in Pakistan. Only weeks ago, Pakistani public opinion was hostile to an open fight against internal militants, terming this “America’s war.”

But in the last month, the Pakistani Taliban’s tactics – blowing up mosques and markets – have turned the public there against the militants. Obama’s speech captured that sentiment and stressed the common interests of Pakistanis and Americans in countering such barbarity. It created a possibility (no guarantees) the Pakistani public will now support open U.S. cooperation with Pakistan’s army against the militants. Obama’s speech placed Americans and Pakistanis on the same side.

Similarly, Lebanese pundits credit Obama’s speech with helping a U.S.-backed coalition prevent an expected victory by a Hezbollah-led coalition in Lebanese elections on June 7. “Lebanon is a telling case,” Osama Safa, director of a Lebanese think tank, told the New York Times. “It is no longer relevant for the extremists to use the anti-American card.”

In Iran, Ahmadinejad has claimed victory in an election many Iranians believe was blatantly stolen. Obama’s speech made it easier for the challenger, Mir Hussein Mousavi, to denounce Ahmadinejad’s foreign policy. It will make it harder for the Iranian leader to use the American bogeyman as an excuse for future repression.

One speech cannot guarantee change. But it can open the door to new possibilities. In that sense, Obama’s Cairo effort definitely hit the mark.

Trudy Rubin is a columnist and editorial board member for The Philadelphia Inquirer. Her e-mail address is: trubin@phillynews.com.