On a regional tour devoted to a suddenly-changed Syria, the top US diplomat flew to Baghdad from the Turkish capital Ankara and headed into talks with Iraqi Prime Minister Mohammed Shia al-Sudani.
Blinken said he told Sudani of "our commitment to working with Iraq on security and always working for Iraq's sovereignty, to make sure that that is strengthened and preserved".
"I think this is a moment as well for Iraq to reinforce its own sovereignty as well as its stability, security and success going forward," Blinken said.
He added that "no one knows the importance" more than Iraq of stability in Syria and avoiding the resurgence of Islamic State group (IS) jihadists, also known by the Arabic acronym Daesh.
"We are determined to make sure that Daesh cannot re-emerge," Blinken said.
"The United States (and) Iraq, together had tremendous success in taking away the territorial caliphate that Daesh had created years ago."
The Islamic State group (IS) overran large swathes of Iraq and neighbouring Syria in 2014, proclaiming its "caliphate" and launching a reign of terror.
It was defeated in Iraq in 2017 by Iraqi forces backed by a US-led military coalition, and in 2019 lost the last territory it held in Syria to US-backed Kurdish forces.
Iraq is keen to prevent any spread of chaos from Syria, where on Sunday Islamist-led rebels toppled the five-decade rule of the Assad dynasty following a lightning offensive.
Sudani, in his meeting with Blinken, "underscored the necessity of ensuring the representation of all components of the Syrian people in managing the country to bolster its stability," Sudani's office said.
He stressed Iraq "expects tangible actions, not just words" from Syria's transitional authorities, and "emphasised the importance of preventing any aggression on Syrian territories by any party".
After taking a helicopter into central Baghdad, Blinken also complimented Iraq on a construction boom, saying it showed growing success.
US troops
Iraq's government has urged respect for the "free will" of all Syrians and the country's territorial integrity after Assad's fall.
The deposed Syrian leader hailed from a rival faction of the Baath party of Iraqi dictator Saddam Hussein, ousted in a 2003 US-led invasion.
The United States maintains about 2,500 troops in Iraq and 900 more in Syria as part of a campaign to prevent IS resurgence.
President Joe Biden's administration has agreed with Iraq to end the coalition's military presence by September 2025 but stopped short of a complete withdrawal of the US forces, whose presence has been opposed by Iran-aligned armed groups in Iraq.
President-elect Donald Trump takes office next month and has long been sceptical of US troop deployments, although it remains unclear whether he would backtrack from Biden's agreement or change tactics in light of developments in Syria.
Last Saturday, the day before rebels took control of Damascus, Trump on his Truth Social platform called Syria "a mess," and added: "THE UNITED STATES SHOULD HAVE NOTHING TO DO WITH IT. THIS IS NOT OUR FIGHT."
Blinken has pushed for an "inclusive" political process to bring an accountable government to Syria and avoid sectarian bloodletting of the sort seen in Iraq after the fall of Saddam.
In Baghdad, he said he spoke with Sudani about the conviction of many countries that "as Syria transitions from the Assad dictatorship to hopefully a democracy, it does so in a way that... protects all of the minorities in Syria, that produces an inclusive, non-sectarian government and does not become in any way a platform for terrorism".
Speaking in Jordan on Thursday, Blinken said all regional players he had spoken to "agreed on the need to have a unified approach to advance many of our shared interests" in Syria.
Turkey strongly opposes the US alliance with Syrian Kurdish fighters, who assist the United States with the fight against the Islamic State group but whom Ankara links to outlawed Kurdish separatists at home.
Israel in turn has been pounding Syria, decimating military sites across its historic adversary after a deadly campaign against the Iranian-backed Hezbollah militia in Lebanon, aiming in part to curb the regional influence of Tehran which had allied itself with Assad.
