To fight terrorism of the kind that brutalized Mumbai, India, President-elect Barack Obama should retain James Glassman, the Bush administration’s commander in the “war of ideas” against extremism.

[IMGCAP(1)]In just six months in office, Glassman has invigorated and modernized U.S. programs to not just improve America’s image in the world, but confront radical ideologies, including on the Internet.

Glassman, undersecretary of State for public diplomacy, refused in an interview to disclose specifically what the government is doing in response to the Mumbai massacre, but it’s a fair bet that it’s stimulating and amplifying moderate Islamic expressions of disapproval of the attacks.

Longer term, Glassman has helped finance expansion of a private faith-based program to convert Pakistani religious schools — madrassas — from extremist training grounds into academic institutions.

This week in New York, he convened a conference of young bloggers from around the world who have been fighting violence — including one who swiftly stimulated mass rallies of millions of people to oppose the Colombian terrorist group FARC.

Keeping on a conservative Republican like Glassman — formerly based at the American Enterprise Institute — may be a hard swallow for Democrats eager to occupy plum jobs. Any number have experience in public diplomacy.

But before they oust him, they ought to listen to him, take his recommendations for beefing up the U.S. global communications infrastructure and — for sure — maintain his innovations.

(Disclosure: Glassman and I have been friends for 30 years and, as editor of Roll Call, he hired me in 1991.)

The point for Obama’s national security team, though, is that Glassman has redefined the concept of public diplomacy in several dramatic ways — one of which is “public diplomacy 2.0,” whereby the United States now successfully challenges al-Qaida on the Internet.

The terrorist group formerly had the upper hand, using Web sites and often-gruesome videos to propagandize against the West, exhort followers and even plan attacks.

As Glassman said this week at a briefing at the New America Foundation, “the Internet world of al-Qaida is one direction: Believe this. Do that.

“The Internet world of today is one of interactivity and conversation: ‘I think this. Your ideas are unconvincing. I need more information to make up my mind.’ …

“This new virtual world is democratic. It is an agora. It is not a place for a death cult that counts on keeping its ideology sealed off from criticism. The new world is a marketplace of ideas and it is no coincidence that al-Qaida blows up marketplaces.”

In keeping with the Obama campaign’s pioneering use of social networking sites — Facebook, Twitter, YouTube — Glassman has got the U.S. government sponsoring worldwide Internet debates and film contests on subjects such as democracy, culture and human rights.

Glassman’s primary change in how America communicates with the world was to shift emphasis from sometimes-defensive efforts to improve America’s image to a “war of ideas” against Islamic groups.

“Some people don’t like the term ‘war of ideas’ because it sounds us-against-them, but look at it this way: There’s clearly a war of bombs and bullets going on.

“Secretary of Defense (Robert) Gates has said we can’t kill or capture our way to victory. So what we do is fight this war with ‘soft power,’ with ideas, images, words and deeds.”

His war has two objectives — to discredit radical groups and their ideologies and divert young people from paths that lead to extremism.

On its own, al-Qaida has contributed to its own discrediting by killing fellow Muslims, including beheading women and children, which is increasingly denounced by clerics, governments and media.

Even the Arab cable channel Al-Jazeera, Glassman said, “is no longer a cheerleader for al-Qaida,” though it still is often anti-American.

Glassman reorganized the U.S. government interagency process for countering terror groups into a Global Strategic Engagement Center, with input from the State and Defense departments, the CIA and the National Counterterrorism Center.

Among other things, that group has developed public diplomacy plans for crucial countries like Afghanistan and makes sure that the world knows about extremist misdeeds such as Taliban atrocities.

Glassman has only $50,000 to conduct “war of ideas” combat, but he’s using as much as he can of his office’s total budget of $900 million — which he says should be doubled — on direct “traditional public diplomacy programs” such as English-teaching, exchanges and training of teachers and journalists, to focus on young people vulnerable to extremist recruitment.

In Pakistan, for example, the private International Center for Religion and Diplomacy is able to work with only 15 percent of Pakistan’s madrassas.

Glassman said the group could help re-program all of them with just $50 million. “But I don’t have $50 million,” he said. The U.S. finances English teaching to 400 Pakistani students. “We’d like to do 1,000 or 2,000,” he said.

Glassman said that Obama has wisely advocated establishing a “national security budget” covering the entire range of foreign and military programs. Glassman advocates devoting more to “soft power” programs.

Democrats habitually advocate “soft power” — diplomacy, foreign aid, education and (sometimes) trade — to advance America’s interests, as opposed to military “hard power.”

Glassman has invented ways to give “soft power” a hard, smart edge. The Obama team should keep him — or, at least, adopt his ideas.