"We are just heartsick at this loss of life in the line of duty," a subdued Clinton said in a statement to reporters after the rally.
The New York senator and Democratic presidential candidate canceled her next appearance in Fort Worth, Texas, telling about 2,000 people who had gathered outside the Tarrant County courthouse that it would be inappropriate to campaign in the wake of the officer's death.
Instead, she went to Methodist Medical Center, where she planned to visit with the officer's family.
"It is important that we respect and appreciate their service," she said. "I certainly am grateful for all they do for me."
Senior Corporal Victor Lozada Tirado died after apparently crashing into a concrete barrier along a viaduct near downtown Dallas, said Lt. Vernon Hale, a police spokesman. Aerial video showed wreckage scattered for several yards.
The officer was in the rear of the motorcade, following it as it took a turn not far from Dealey Plaza, where John F. Kennedy was assassinated in 1963.
Video: Clinton motorcade officer dies Asked if police had enough lead time to plan a safe route, Hale said, "It doesn't matter with our guys. They've been doing this so long. Of course, we already had one tragedy in Dallas."
Lozada Tirado joined the Dallas police force in December 1988. He was married with four children, two boys and two girls.
Sen. Barack Obama asked for a moment of silence in memory of Lozada Tirado at a rally in Corpus Christi later in the day. He said the officer had been in his own detail two days ago in Dallas.
"It's a reminder of the outstanding work that law enforcement does for us each and every day," he said.
In August 2006, an Albuquerque, N.M., police officer in President Bush's motorcade died in a motorcycle crash. Germaine Casey, 40, died on Aug. 27 when he crashed as Bush returned to the airport after a fundraiser for Sen. Pete Domenici, R-N.M.
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