DETROIT (Reuters) - Republican Jeb Bush stumbled on foreign policy in a big speech on Wednesday, telling a crowd that American diplomats have been withdrawn from Yemen, when in fact not all of them have been.

Pressure from Islamic militants in the country has led to a diplomatic drawdown in the Yemeni capital of Sanaa. While the U.S. embassy has stayed open, routine consular services to the public were halted.

Bush, at the Detroit Economic Club, criticized President Barack Obama's handling of the Islamic State threat and cited the case of Yemen.

"As we pull back from the Middle East, look what happened. Look what happened with ISIS in Syria. Look what happened with ISIS in Iraq. The big, huge victory in Yemen that the president has talked about lasted about six months. Now we've closed the ... there are no embassy personnel in Yemen's capital. So we have to be engaged. And that doesn't necessarily mean boots on the ground in every occurrence," Bush said.

The speech was the first in a series aimed at defining why he is considering a run for the Republican presidential nomination and what policies he would pursue if elected.

Bush is viewed as a front runner in the Republican race now that 2012 nominee Mitt Romney has decided against a third White House run. Bush leads national polls over a crowded field of potential rivals, including Wisconsin Governor Scott Walker and New Jersey Governor Chris Christie. 

(Reporting by Steve Holland; Editing by Jeffrey Benkoe)