The increase is in addition to 14,000 American soldiers sent into the region since May.
President Donald Trump warned that Iran "would be held fully responsible" after the US Embassy in Baghdad was stormed by protesters on Tuesday, before ordering that 750 US soldiers would be sent to the Middle East with 3,000 more preparing for deployment in the next few days.
Trump warned Iran that it would pay a "big price" for "lives lost, or damage incurred" during the protests, which followed deadly US airstrikes this week that killed 25 fighters from an Iran-backed Shiite militia in Iraq.
Shouting “Down, Down USA!” the crowd - many of them Iran-supported militiamen - tried to push inside the embassy grounds, hurling water bottles and smashing security cameras outside. No US casualties have been reported after the incident.
The US military carried out the strikes Sunday against the Iranian-backed Kataeb Hezbollah militia, calling it retaliation for last week's killing of an American contractor in a rocket attack on an Iraqi military base that it blamed on the group.
The US attack — the largest targeting an Iraqi state-sanctioned militia in recent years — and the calls for retaliation, represent a new escalation in the proxy war between the US and Iran playing out in the Middle East.
It was not clear where the US soldiers would be deployed, but an official told AP that they would be based in Kuwait, a staging point for American operations inside Iraq. The 750 are in addition to the 14,000 US troops that have been deployed to the region amid heightened tensions with Tehran.
Tuesday's attempted embassy storming took place after mourners held funerals for the militia fighters killed in a Baghdad neighbourhood, after which they marched on to the heavily fortified Green Zone and kept walking till they reached the sprawling US Embassy.
Security guards were seen retreating to the inside of the embassy. Protesters also were seen hanging yellow flags belonging to the Kataeb Hezbollah militia backed by Iran on the walls of the embassy.
US Secretary of State Mike Pompeo said the strikes send the message that the US will not tolerate actions by Iran that jeopardise American lives.
The Iranian-backed Iraqi militia had vowed Monday to retaliate for the U.S. military strikes in Iraq and Syria that killed 25 of its fighters and wounded dozens. The attack and vows for revenge raised concerns of new attacks that could threaten American interests in the region.
The US attack outraged both the militias and the Iraqi government which said it will reconsider its relationship with the US-led coalition — the first time it has said it will do so since an agreement was struck to keep some US troops in the country. It called the attack a “flagrant violation" of its sovereignty.
In a partly televised meeting Monday, Iraqi Prime Minister Adel Abdul-Mahdi told Cabinet members that he had tried to stop the US operation “but there was insistence" from American officials.
The US military said "precision defensive strikes" were conducted against five sites of Kataeb Hezbollah, or Hezbollah Brigades in Iraq and Syria. The group, which is a separate force from the Lebanese militant group Hezbollah, operates under the umbrella of the state-sanctioned militias known collectively as the Popular Mobilization Forces. Many of them are supported by Iran.