Mr Bouteflika is the first Algerian leader to visit Britain since 1962
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Tony Blair has voiced optimism over the deportation of terror suspects to Algeria after talks with the country's President, Abdelaziz Bouteflika.
The prime minister said he hoped increased co-operation with Algeria would aid the government in its efforts to send deportees back home.
Britain wants assurances that those sent back will not be ill-treated.
President Bouteflika, who is currently on a state visit to the UK, called on the Queen before meeting Mr Blair.
Last month two men were sent back to Algeria on the grounds that they were a threat to national security.
The BBC has learned that the men have been released from custody and have been reunited with their families.
The two suspects were among seven Algerians arrested last September following the 7 July attacks in London.
Unnecessary risk
At a joint press conference, Mr Blair said Algeria's collaboration was important in the fight against terrorism
"I certainly hope that greater co-operation between our countries can facilitate our ability to send people back to Algeria," he said.
"It's important to realise that we all of us - even if in different ways - face the same issues to do with this global terrorism and it's important that we co-operate as much as possible together.
"The single most frustrating thing for me is when we need to be able ... to deport people from this country who are causing trouble here and we are told we can't do so, because that then imposes quite an unnecessary risk on our country."
Some 27 individuals currently await deportation on national security grounds and the largest group is Algerian.
But the process of removing them is stalled while the courts decide whether the possibility of ill-treatment is too great.