Washington (CNN) -- President Barack Obama will give a speech on the Afghanistan troop drawdown on Wednesday, a senior administration official said Monday.

The news came hours after White House Press Secretary Jay Carney told reporters that Obama had yet to make a final decision on the size and scope of the troop withdrawal, but would do so "soon."

"The president is still in a process of finalizing his decision on the pace and scope of the drawdown that will begin in July of 2011," Carney said Monday afternoon. "He's finalizing his decision. He's reviewing the options and the assessments and will have an announcement to make soon."

An estimated 100,000 U.S. troops are serving in Afghanistan, some 30,000 of which are part of the so-called surge ordered in late 2009 in a bid to control the rising violence.

Obama has said those troops would begin coming home in July, and he recently indicated the number would be "significant."

It was not clear then what the president considered significant. White House officials have not elaborated.

The president has repeatedly said he is confident the United States can meet the self-imposed deadline to begin bringing U.S. troops back from Afghanistan without compromising Afghan security, though military commanders and government officials have raised concern about the readiness of Afghan security forces.

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"We have made great strides toward achieving the objectives laid out in the mission that the president articulated in December of 2009," Carney said Monday afternoon. "And he will make his decision based on the need to succeed further in achieving those objectives and to transfer authority gradually, security authority, over to the Afghan national security forces, with an eye to the fact that, as agreed to by NATO in Lisbon, we will eventually transfer full security lead over to the ANSF in 2014."

Nearly three-quarters of Americans polled this month said they support the United States pulling some or all of its forces from Afghanistan.

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That figure jumped 10 points since May, likely as a result of the death of Osama bin Laden, pollsters said.

The CNN/Opinion Research Corp. poll was conducted June 3 through June 7, with 1,015 adult Americans questioned by telephone. The survey's overall sampling error is plus or minus 3 percentage points.

CNN's Tom Cohen contributed to this report.