The United States, whose late Friday strikes killed 45 people, blamed Sunday's drone attack that hit a US base in Jordan on militants backed by Tehran.
US forces however did not strike inside Iranian territory, with both Washington and Tehran seemingly keen to avoid all-out war.
But with tensions already running high in the face of the Israel-Hamas war in Gaza, both the Syrian and Iraqi governments joined Tehran in accusing Washington of undermining regional stability.
National Security Council spokesman John Kirby said US warplanes struck "more than 85 targets at seven facilities", four in Syria and three in Iraq.
"These targets were carefully selected to avoid civilian casualties," he added.
But the Iraqi government said civilians were among at least 16 people killed in the country's west, and Damascus also reported civilian deaths, but a war monitor said all 29 killed in the US strikes on Syria were fighters.
"This aggressive air strike will push the security situation in Iraq and the region to the brink of the abyss," said Iraqi government spokesman Bassem al-Awadi.
Iraqi Prime Minister Mohamed Shia al-Sudani declared three days of mourning, while the foreign ministry said Washington's charge d'affaires in Baghdad was handed a formal protest over the strikes.
Iranian foreign ministry spokesman Nasser Kanani said the overnight strikes would "have no result other than intensifying tension and instability".
Hamas, whose unprecedented October 7 attack on Israel sparked the current spiral of violence in the region, accused Washington of pouring "oil on the fire".
Meanwhile, diplomatic sources said the UN Security Council would convene Monday, after Russia called for a meeting "over the threat to peace and safety created by US strikes on Syria and Iraq".
The Syrian foreign ministry said the strikes served to "inflame the conflict in the Middle East".
- Flurry of attacks -
The Syrian army said "a number of civilians and soldiers" were killed in eastern Syria, but the Syrian Observatory for Human Rights monitor reported no civilian deaths.
The Britain-based Observatory said the strikes killed 29 pro-Iran fighters, including at least six from Lebanese Hezbollah.
The Lebanese group condemned the US operation, saying it "contributes to heightening conflict, tensions and escalation" across the region.
The Observatory earlier said some militant groups had begun evacuating their positions and civilians in the towns of Deir Ezzor and Mayadeen had fled their homes in fear of more US strikes.
Syria's culture ministry condemned a "barbaric" strike on Deir Ezzor province that local media said had damaged a ninth-century citadel.
Biden said the overnight strikes were only a beginning. "Our response... will continue at times and places of our choosing," the US president said.
Washington said it had informed Baghdad "prior to the strikes," drawing an angry denial from the Iraqi government spokesman who called it an "unfounded claim crafted to mislead international public opinion".
Tensions between the two governments have deepened in recent months after Washington carried out previous air strikes in response to a flurry of attacks on US-led troops since the Gaza war began in October.
Washington and Baghdad opened talks on the future of the US-led troop presence late last month after repeated demands from Sudani for a timetable for their withdrawal.
- 'Significant escalation' -
The United States has some 900 troops in Syria and 2,500 in Iraq as part of an international coalition against the Islamic State group.
Its troops in Iraq are deployed at the invitation of Baghdad, but those in Syria are deployed in areas outside government control.
The Syrian military demanded on Saturday that Washington withdraw its troops.
"The occupation of parts of Syrian territory by US forces cannot continue," it said.
Analysts said the US strikes were unlikely to stem the flurry of attacks on US targets sparked by American support for Israel in its war on Hamas.
The strikes represent a "significant escalation," said Allison McManus, of the Center for American Progress think tank, but "we have not seen that similar tit-for-tat strikes have had a deterrent effect."
Al-Nujaba, an Iraqi group part of a pro-Iran alliance blamed by Washington for numerous attacks on its forces, vowed a response.
In a statement, the group warned "the US occupation... that the Islamic resistance will respond in the manner it deems appropriate, at the time and place of its choosing, and that this is not the end".
US and coalition troops have been attacked more than 165 times in Iraq, Syria and Jordan since mid-October.
The soldiers killed Sunday were the first American military deaths from hostile fire in the upsurge of violence.
burs-jsa/ami
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