How many U.S. troops are currently in Iraq?

Following multiple presidential authorizations and varied tallies regarding the number of U.S. troops currently responding to the crisis in Iraq, the Pentagon announced an official number Tuesday.

The U.S. currently has approximately 750 troops in Iraq, the Pentagon says, including 100 that predate the unfolding crisis there and about 650 who have been sent to help protect U.S. personnel and assist the Iraq army on the deteriorating security conditions.

The number of troops sent to deal with the ongoing crisis nearly doubled in the last several days with the addition of 300 military personnel sent to Baghdad Sunday and Monday. That figure could still go up: President Obama has authorized the Pentagon to send up to 770 troops to protect the embassy and advise the Iraqi army in relation to the advance of the Islamic State of Iraq and Syria (ISIS).

Prior to the crisis, there were 100 members from the U.S. Office of Security Cooperation who handle regular arms sales to Iraq.

The troops sent in since the start of the crisis include 470 for security at the U.S. embassy, the Baghdad International Airport, and the route in between.Mr. Obama authorized those forces with two different letters asserting his war powers. The first letter on June 16 authorized up to 275 troops, 170 of whom went to Baghdad. The remaining 100, mainly Air Force personnel to run an evacuation through the airport, remained in Kuwait and moved to Baghdad on Monday.

Mr. Obama authorized a second batch of 200 military personnel for security purposes Monday, including operators and maintainers for Apache helicopters and short-range drones. They were likely not sent as a result of any new threat, CBS News Pentagon Correspondent David Martin reports, but to fully prepare the embassy for an evacuation should that become necessary.

"It continues to be very dangerous, the threat continues to be very real, but we have seen Iraqi security forces in and around Baghdad reinforce themselves and prepare to defend and they are taking the offensive," Pentagon spokesman Rear Adm. John Kirby told reporters Tuesday. "It's a contested environment right now."

The president also authorized up to 300 military advisers for deployment to Iraq on June 26 to assist Iraqi security forces and assess intelligence, surveillance and reconnaissance assets in the region. Of those 300, about 180 had arrived as of Monday, the Pentagon said. Ninety troops are at a joint operations center in Baghdad, and another 90 comprise the assessment and advisory teams. Those teams are expected to report back to the Pentagon in a few weeks.

"There are two separate and distinct mission sets for the troops that are being sent to Iraq," Kirby said. "The first one is security assistance and the second one is assessment teams and the joint operations center. This is...what will eventually become the advisory mission."