In the message, bin Laden praised as a "hero" Nigerian national Umar Farouk Abdulmutallab who allegedly tried to detonate explosives on a Northwest Airlines plane approaching Detroit on December 25 but was foiled by passengers.
"The message that was conveyed through the (attacked) plane of the hero Umar Farouk is to stress earlier messages delivered to you by the heroes of the 11" September attack, he said.
"That (message) is, that America should not dream of security until we enjoy it as a reality in Palestine."
The authenticity of the recording could not immediately be verified, but Al-Jazeera said the voice was bin Laden's and IntelCenter said it appeared to be genuine.
"From Osama to Obama: Had we been able to deliver our messages to you in words, we would not have sent them by planes," the statement said.
"It is not fair that you (America) enjoy a good life while our brothers in Gaza endure the worst standard of living. Therefore, God willing, our attacks against you will continue as long as you maintain your support to Israel."
IntelCenter said it considered bin Laden's choice of the phrase "Peace be upon those who follow guidance" as "a possible indicator of an upcoming attack" in the next 12 months.
Al-Qaeda in the Arabian Peninsula (AQAP) had claimed responsibility for the Christmas Day plane attack, and analysts said bin Laden through his statement is stressing he is still in overall control of the network.
Washington has accused AQAP of training Abdulmutallab, who spent some time in Yemen.
The US administration is putting pressure on Yemen to clamp down on Al-Qaeda militants in the impoverished country, and an international meeting to discuss militancy in Yemen will be held on January 27 in London.
British Foreign Secretary David Miliband said the foiled Christmas attack marks a "new phase" in Al-Qaeda's campaign against the West.
"The heart of the Al-Qaeda senior leadership remains on the Afghan/Pakistan border," Miliband said, echoing the view held by many security experts about their whereabouts.
"But there is a real issue in Yemen -- the fact that Al-Qaeda in the Arabian Peninsula should have tried to strike in Detroit marks a new phase in the campaign and that's why there's an important meeting on Yemen on Wednesday."
Yemen has intensified its campaign against Al-Qaeda, launching waves of air strikes on the extremists' hideouts, and insists it can battle the group on its own, without any foreign military intervention.
Sanaa stopped granting visas to foreigners at airports on Thursday in a bid to curb a feared inflow of militants, believed to be training with Al-Qaeda.
The US Senate Foreign Relations Committee released a report this week warning AQAP might be training as many as three dozen Americans who converted to Islam in prison.
Intelligence reports have pointed for some time at Yemen as a new hub for Al-Qaeda fighters as pressure increases on them in Afghanistan and Pakistan.
Michael Leiter, director of the US National Counterterrorism Center, told lawmakers in September that Yemen could become a base for Al-Qaeda to train and plot anti-US attacks.
Analysts believe the problems facing Yemen, including a Shiite rebellion in the north, secessionism in the south, and poverty, create a perfect environment for Al-Qaeda to thrive.
A US grand jury has indicted 23-year-old Abdulmutallab on six counts arising from the attempt to blow up the jet packed with 279 passengers and 11 crew on Northwest Airlines Flight 253 from Amsterdam.
Bin Laden, who has a 50-million-dollar bounty on his head, last made a public statement four months ago when he was quoted as urging European countries to withdraw their forces from Afghanistan.