"The current main challenge is Ukraine," Rasmussen said in advance of his Utah visit.
But it is not the only focus.
"We need a strong American presence in Europe. And we need it in the Middle East. That's indispensable," said the former prime minister of Denmark, who was NATO secretary general from 2009 until last year.
More resources, he added, are also needed to fight the Islamic State and to strengthen NATO members' defense against cyberattacks.
During his tenure at NATO, Rasmussen oversaw efforts to stabilize Afghanistan and provide military aid to Libyan rebel forces in 2011.
He has been to Salt Lake City once before, about 15 years ago.
"It's a wonderful state and a wonderful city," Rasmussen said.
On this trip, the U. is not the only college he is scheduled to visit. California's Stanford University also is on the agenda, alongside appointments in Washington, D.C., and New York City.
The U.S. tour is unlikely to be totally devoid of business.
Rasmussen recently became a consultant for Goldman Sachs, as information on its purchase of a stake in a Danish public utility is set to emerge. He is guiding Goldman through the release of documents related to the deal with Dong Energy A/S, set to be unsealed by the Danish government.
"Goldman Sachs has nothing to hide," Rasmussen said. Being "as open as possible," he added, "is always the best approach."
If you go
"Unlimited Partnerships: The European Union and the United States" at the Utah Museum of Fine Arts, Dumke Auditorium, 410 Campus Center Drive. Event starts at 11 a.m.