The demonstrators entered the heavily fortified Green Zone and prepared tents to hold a sit-in protest, an official from the Iraqi Interior Ministry told Xinhua news agency.
The US strikes on the Kataib Hezbollah (KH) militia group, a faction of the Iraqi Popular Mobilization Forces (PMF), took place on Sunday after an attack earlier this week on an Iraqi base near Kirkuk province killed an American civilian contractor.
In response, Iraq has announced that it would summon the American Ambassador in Baghdad.
The Foreign Ministry said in a statement on Monday that "the attack is seen as a blatant violation of the sovereignty of Iraq, and a condemned act, which is rejected by all norms and laws that governing relations between states".
It asserted that Iraq, as an independent country, will not allow its land to be a battlefield, or to be a passage to carry out attacks on others, according to the statement.
The US Ambassador in Baghdad will be summoned to be informed of Iraq's stance, and Iraq will discuss with the European partners in the international coalition against the Islamic State (IS) "to come out with a unified position regarding the mechanisms of work and the future presence of the coalition forces in Iraq", the statement added.
KH commander, Abu Mahdi al-Muhandis, warned that the militia's response "would be very tough on the American forces in Iraq".
( With inputs from IANS )