In a speech in Chicago, the former Florida governor outlined a broad strategy of projecting American power and addressing “the shortfalls in our defense spending”.
Jeb Bush also criticized President Barack Obama for an “inconsistent and indecisive” foreign policy.
He is one of several Republicans expected to run for president in 2016.
Jeb Bush is the brother of former President George W. Bush and son of former President George H.W. Bush.
He has developed campaign infrastructure but has not officially said he is running.
In the speech to the Chicago Council on Global Affairs, Jeb Bush says he has been “lucky” to have family who “shaped America’s foreign policy from the Oval Office”.
“I recognize that as a result, my views will often be held up in comparison to theirs,” Jeb Bush said.
“But I am my own man – and my views are shaped by my own thinking and own experiences.”
The Washington Post reported 19 of 21 Jeb Bush’s foreign policy advisors are pulled from his brother and father’s administrations, although many were also considered as advisors to Mitt Romney before he backed out of a run.
Jeb Bush has demurred from answering whether he believes his brother’s choice to go to war in Iraq was appropriate.
During the speech, he criticized Barack Obama as someone who “has left America less influential in the world”.
“I believe fundamentally that weakness invites war … and strength encourages peace,” Jeb Bush said.
Jeb Bush also expressed concern over negotiations with Iran over its nuclear programme and backed the National Security Agency’s bulk collection of telephone metadata records of Americans.
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