* Five militants captured alive
* Hostage death toll to rise from provisional 23 - minister
* France, Britain defend Algerian response
* Algeria says gas plant to restart in two days
By Lamine Chikhi and Abdelaziz Boumzar
ALGIERS/IN AMENAS, Algeria, Jan 20 (Reuters) - A veteran Islamist fighter claimed responsibility on behalf of al Qaeda for the Algerian hostage crisis, a regional website reported on Sunday, tying the bloody desert siege to France's intervention across the Sahara in Mali.
Algeria said it expected to raise its preliminary death tolls of 23 hostages and 32 militants killed in the four-day siege at a gas plant deep in the Sahara. It said on Sunday it had captured five militants alive.
Western governments whose citizens died or are missing have held back from criticising tactics used by their ally in the struggle with Islamists across the vast desert.
"We in al Qaeda announce this blessed operation," one-eyed guerrilla Mokhtar Belmokhtar said in a video, according to the Sahara Media website, which quoted from the recording but did not immediately show it.
"We are ready to negotiate with the West and the Algerian government provided they stop their bombing of Mali's Muslims," said Belmokhtar, a veteran of two decades of war in Afghanistan and the Sahara.
Belmokhtar's fighters launched their attack on the In Amenas gas plant before dawn on Wednesday, just five days after French warplanes unexpectedly began strikes to halt advances by Islamists in neighbouring northern Mali.
European and U.S. officials say the raid was almost certainly too elaborate to have been planned since the start of the French campaign, although the military action by Paris could have provided a trigger for an assault prepared in advance.
"We had around 40 jihadists, most of them from Muslim countries and some even from the West," Sahara Media quoted Belmokhtar as saying. Algerian officials say Belmokhtar's group was behind the attack but he was not present himself.
Some Western governments have expressed frustration at not being informed in advance of the Algerian authorities' decision to storm the complex on Thursday.
Survivors have said many hostages were killed when Algerian government forces blasted a convoy of trucks on Thursday morning. Algerian officials said they stormed the compound because the militants were trying to escape with their captives.
Britain and France both defended the Algerian action.
"It's easy to say that this or that should have been done. The Algerian authorities took a decision and the toll is very high but I am a bit bothered ... when the impression is given that the Algerians are open to question. They had to deal with terrorists," French Foreign Minister Laurent Fabius said.
British Prime Minister David Cameron said in a televised statement: "Of course people will ask questions about the Algerian response to these events, but I would just say that the responsibility for these deaths lies squarely with the terrorists who launched this vicious and cowardly attack.
"We should recognise all that the Algerians have done to work with us and to help and coordinate with us. I'd like to thank them for that. We should also recognise that the Algerians too have seen lives lost among their soldiers."
With so much still unknown about the fates of foreigners held at the site, some countries that have faced casualties have yet to issue full counts of their dead.
Scores of foreigners lived alongside the hundreds of Algerians at the plant, which was run by Britain's BP and Norway's Statoil and also housed workers from a Japanese engineering firm and a French catering company.
Cameron said three British nationals were confirmed killed and another three plus a British resident were also feared dead. One American has been confirmed killed. Statoil said it was searching for five missing Norwegians. Japanese and French citizens are also among those missing or presumed dead.
Algeria's Interior Ministry, which gave the figure on Saturday of 23 hostages killed, said 107 foreign hostages and 685 Algerians had been freed.
"I am afraid unfortunately to say that the death toll will go up," Minister of Communication Mohamed Said was quoted as saying on Sunday by the official APS news agency. Private Algerian television station Ennahar said on Sunday 25 bodies had been discovered. Clearing the base would take 48 hours, it said.
Survivors have given harrowing accounts. Alan Wright, now safe at home in Scotland, told Sky News he had escaped with a group of Algerian and foreign workers who hid for a day and a night and then cut their way through a fence to run to freedom.
While hiding inside the compound the first night, he managed briefly to call his wife who was at home with their two daughters desperately waiting for news.
"She asked if I wanted to speak to Imogen and Esme, and I couldn't because I thought, I don't want my last ever words to be in a crackly satellite phone, telling a lie, saying you're OK when you're far from OK," he recalled.
Algeria's oil minister, Youcef Yousfi, visited the site and said the physical damage was minor, state news service APS reported. The plant, which produces 10 percent of Algeria's natural gas, would start back up in two days, he said.
OIL VULNERABILITIES EXPOSED
The Islamists' assault has tested Algeria's relations with the outside world and exposed the vulnerability of multinational oil operations in the Sahara.
Algeria, scarred by the civil war with Islamist insurgents in the 1990s which claimed 200,000 lives, has insisted there would be no negotiation in the face of terrorism.
France especially needs close cooperation from Algeria to have a chance of crushing Islamist rebels in northern Mali. Algiers has promised to shut its porous 1,000-km border with Mali to prevent al Qaeda-linked insurgents simply melting away into its empty desert expanses and rugged mountains.
Algeria's permission for France to use its airspace, confirmed by Fabius last week, also makes it much easier to establish direct supply lines for its troops which are trying to stop the Islamist rebels from taking the whole of Mali.
French troops in Mali advanced slowly on Sunday towards the town of Diably, a militant stronghold the fighters abandoned on Saturday after punishing French attacks.
According to Communications Minister Said, the militants were of six different nationalities. Believed to be among the dead was their leader, Abdul Rahman al-Nigeri, a fighter from Niger who is seen as close to Belmokhtar.
The apparent ease with which guerrillas swooped in from the desert to take control of an important energy facility has raised questions over the country's outwardly tough security measures. Yousfi said Algeria would not allow foreign security firms to guard its oil facilities.
Algerian officials said the attackers may have had inside help from among the hundreds of Algerians employed at the site.
Security in the half-dozen countries around the Sahara desert has long been a preoccupation of the West. Smugglers and militants have earned millions in ransom from kidnappings.
The most powerful Islamist groups operating in the Sahara were severely weakened by Algeria's secularist military in the civil war in the 1990s. But in the past two years the regional wing of al Qaeda has gained fighters and arms as a result of the civil war in Libya, when arsenals were looted from Muammar Gaddafi's army.