Japan called for an end to the raid, summoning the Algerian ambassador to express concern for the lives of the captives and to plead for up-to-date information.
British Prime Minister David Cameron said he was "disappointed" not to have been told about the raid in advance.
But while many details of how events at the In Amenas plant have unfolded remain unclear, Algeria's decision to deal with the kidnappers forcefully and unilaterally fits with a deeply-entrenched and uncompromising approach to counter-terrorism.
"I'd be surprised if they'd reacted any other way," said Jon Marks, an Algeria analyst and head of the Cross-border Information consultancy.
"From the Algerian point of view the attackâ€¦ was an affront to the prestige of the Algerian military which is a very central part of the Algerian value system."
The military is still seen as the ultimate arbiter of power in Algeria, and has never been placed fully under civilian control.
The army, and the governments it supports, derive much of their legitimacy from largely winning the military battle against Islamist insurgents in the 1990s, during a vicious conflict that left as many as 150,000 people dead.
Algerian authorities have expressed some bitterness that they were left to fight this conflict on their own, before most of the rest of the world was confronted with the threat from Islamist militancy.
But they also take pride in their counter-terrorism experience, their military suppression of armed groups and their publicly-stated reluctance to negotiate or pay ransoms.
"We say that confronted with terrorism, yesterday as today and tomorrow, there will be no negotiation, no blackmail, no let-up in the fight against terrorism," said Algerian Communications Minister Mohamed Said Belaid.
"Those who think we will negotiate with terrorists are delusional."
The conflict in the 1990s was fought in the north of Algeria. Armed groups have only become more active in Algeria's vast southern desert and neighbouring Sahel states in recent years.
They have carried out kidnappings, mainly outside Algeria, and have never launched a major attack on the oil and gas industry that has long been the backbone of Algeria's economy.
However, both the alleged organiser of Wednesday's attack, Algerian militant Mokhtar Belmokhtar, and the prospect of a drawn-out kidnapping saga, are darkly familiar to the Algerian authorities.
"They know Mokhtar Belmokhtar and his gang very well and they know very well that these are people who are extremely adept at operating in the Sahara regions," said Jon Marks, referring to reports that the Algerians intervened when some of the kidnappers and hostages tried to leave the plant.
The risk, he said, was that they would take the hostages to a remote part of the desert and then negotiate for ransoms or prisoner exchanges, "and they used the bluntest of instruments, which was air power, to stop those cars".
"With the western governments you've got the view which is predominant that they've got a duty of care towards the hostages," he added. "Whereas in the perception of those people running the operation, it was very much, 'you must deal with the terrorists and not allow this to happen'."
Mr Cameron said the Algerian prime minister had told him that the military had "judged there to be an immediate threat to the lives of the hostages and had felt obliged to respond".
But beyond this explanation, the Algerians appear to have made little initial attempt to consult, let alone reach out for foreign help or advice. British offers to assist the Algerians were reportedly declined.
"Algeria's not a country that would feel comfortable relying on foreign security forces to help liberate the hostages, and that's because of this deep-seated feeling that there should be no foreign military presence in the country," said Robert Parks, director of the Centre for North African Studies in Algeria.
"This goes back to old principles from right after independence of non-intervention. Algerians are very touchy when it comes to questions of national sovereignty. So it was pretty clear from the start that this was going to be resolved by the Algerians only."
Algeria initially opposed international intervention against Islamist militants in northern Mali, though when France - the former colonial power in both Mali and Algeria - intervened last week, Algeria agreed to open its airspace.
But an attack on Algerian soil was a different matter. The fact that the target of the attack was a gas plant operated in part by foreign companies may have made Algeria particularly keen to tackle the problem on its own terms.
The idea that the Algerian elite and their foreign allies might be the main beneficiaries of large oil and gas profits is a common complaint among Algerians.
"It's important for [the authorities] to show to a domestic audience that they're not beholden to the international community, that they actually control their own hydrocarbon resources - that they're not just a puppet government," said Mr Parks.
Algeria's military intervention against kidnappers at a Saharan gas plant apparently came as a surprise to those foreign governments whose citizens were being held hostage.