Mr Karzai said two suicide bombings that killed 19 people on Saturday – one outside the defence ministry and the other near a police checkpoint – show the group is conducting attacks to show international forces will still be needed after their combat mission ends in 2014.
He said: "The explosions in Kabul and Khost yesterday showed that they are at the service of America.
"They are trying to frighten us into thinking that if the foreigners are not in Afghanistan, we would be facing these sorts of incidents."
Mr Karzai is known for making incendiary comments. In previous speeches he has threatened to join the Taliban and has called his Nato allies "occupiers".
His latest remarks come as his government is negotiating with the US for the long-term presence of US forces in Afghanistan and days after an agreement fell through aiming to transfer the US prison near Kabul to Afghan control.
Mr Karzai said in his speech that any foreign powers that want to keep troops in his country needs to meet conditions set by Afghanistan.
He said: "We will tell them where we need them, and under which conditions.
"They must respect the national sovereignty of our country and must respect all our customs."
Mr Karzai offered no proof, but said the Taliban and the US were in "daily negotiations" in various foreign countries.
Mr Karzai said he did not believe the Taliban's claim they launched yesterday's attacks to show they are still a potent force.
He said: "Yesterday's explosions, which the Taliban claimed, show that in reality they are saying they want the presence of foreigners in Afghanistan."
However, the top American commander in Afghanistan rejected Karzai's allegations as categorically false.
US and Nato forces commander General Joseph Dunford said Mr Karzai had never expressed such views to him.
He said: "We have fought too hard over the past 12 years, we have shed too much blood over the last 12 years, to ever think that violence or instability would be to our advantage."
Mr Karzai also denounced the arrest of a university student yesterday by Afghan forces his aide said were working for the CIA.
It was unclear why the student was detained.
Presidential spokesman Aimal Faizi said the CIA freed the student after Mr Karzai's staff intervened, but that Mr Karzai wants the Afghan raiders arrested.
The president also issued a decree banning all foreign forces from universities and schools unless they obtain prior permission from the Afghan government.
Mr Faizi said the raiders fired shots as they grabbed the student from a Kandahar university and blindfolded him before taking him for interrogation at a CIA post that Taliban leader Mullah Omar once used as a home.
The CIA has trained an Afghan counter-terrorist force several thousand strong, known as the Counterterrorism Pursuit Team, that works mostly in insurgent strongholds in southern and eastern Afghanistan.
US officials say they work with the Afghan intelligence service, but Mr Karzai frequently complains he lacks oversight over their operations.