His remarks come after an audio tape said to be from al Qaeda leader Osama Bin Laden claimed responsibility for the Christmas Day airline bombing attempt in Detroit.
Loading article content
Mr Miliband said the attack demonstrated “the links that can exist between different terrorist groups”.
But he said he would wait to see whether the tape was authentic.
The short recording purporting to be from bin Laden warned US President Barack Obama of further attacks against the US.
“The message delivered to you through the plane of the heroic warrior Umar Farouk Abdulmutallab was a confirmation of the previous messages sent by the heroes of the September 11,” it said.
On Christmas Day, Nigerian national Abdulmutallab attempted to blow up the Northwest Airlines flight he was sitting on as it approached Detroit Metro Airport. But the bomb he was hiding in his underwear failed to explode.
He told police shortly afterward he had been trained and instructed in the plot by al Qaeda operatives in Yemen.
Mr Miliband said he believed that “a significant part of the al Qaeda senior leadership” had been killed.
“But the danger remains very real,” he said.
“You’ve seen this week that the Home Secretary has thought it right to raise the threat level back to the level it’s been for most of the period since 9/11.”
He added: “It remains the case that we need to be extremely vigilant.”
Alan Johnson upped the threat level from “substantial” to “severe” on Friday night - meaning an attack is “highly likely”.
The Home Office said it was unable to comment on any link between the changed threat level and reports that al Qaeda terrorist cells may have trained women, who may not have Arabic appearances, to carry out suicide bomb attacks. The Home Office insisted the threat level was raised only in consideration of an “entire body” of information.
Mr Miliband said it would “very stupid” of him to comment on the intelligence behind the change.
“The fact is though that these people will stop at nothing; they will try every trick in the book, they will use advanced technology, they will use all the mechanisms of open society that we depend on for their own terrible purposes.
“And they will try to strike Christians, Muslims, Jews randomly.”
The shadow home secretary Chris Grayling said he was “entirely supportive” of the Government’s actions.
The Christmas Day bomb plot moved the focus of the fight against terror on to Yemen, where Abdulmutallab reportedly claimed he was supplied with explosives.
Following the attack, the Yemeni government has stepped up a US-backed military operation against al Qaeda sympathisers based in remote areas of the Middle Eastern country.
Mr Miliband said the heart of the al-Qaeda senior leadership remained on the Afghanistan-Pakistan border - but there was a “real issue” in Yemen.
A meeting to discuss the situation in Yemen, called by Gordon Brown, will take place in London on Wednesday, attended by representatives of the Yemeni government, regional powers and Britain’s allies, probably including US Secretary of State Hillary Clinton.