Mr Bush also held out the prospect of a sharp turn in American policy towards China if he became president.
"China is a competitor, not a strategic partner," he said, to loud applause.
"Strategic partner" is the formulation used by the Clinton administration to describe the nature of US relations with China. Mr Bush said that China "must have no illusions about American power and purpose" and pledged continued support for Taiwan.
"We will help Taiwan defend itself," he vowed.
The Governor of Texas was speaking at the Reagan memorial library in California, with Nancy Reagan in the audience. And he pressed a host of Reaganite buttons in the course of a 40-minute speech.
On Russia, which Mr Bush said had gone from "deliverance" to "disappointment" in the past decade, he stressed the dangers from uncontrolled nuclear weapons, and advocated a halt to international loans so long as the money continued to go to the corrupt elite.
He called on Europe to invest more in its own defence and "where necessary in military conflicts", but also promised that the United States would consult more, and stressed that the United States should seek to spread its "principles, not its culture".