Officials say the anthrax was refined for use as a weapon
Mr Daschle said FBI investigators had concluded that the anthrax strain was "a very potent form of anthrax that clearly was produced by someone who knew what he or she was doing".
More than 20 people in Mr Daschle's office have now reportedly tested positive for exposure to anthrax.
The FBI has said that the handwriting was the same on the letter sent to Mr Daschle and another sent to NBC news anchor Tom Brokaw.
They both contained the messages "Death to America" and "God is great".
Potential sources
Investigators say there are hints but no hard evidence as to where the anthrax could have come from.
"Usually to produce that quality of anthrax requires a fairly high level of technological sophistication, which to my mind indicates some sort of state sponsorship," he said.
White House spokesperson Ari Fleischer said that the anthrax could not have come from America itself as US supplies of the bacteria were destroyed as part of the 1972 Biological Weapons Convention.
However at least ten other countries may have access to such biological agents, including Iraq and Iran.
Terrorists could also have obtained access to the bacteria via the many global laboratories that stock it for research purposes.
Fighting bioterrorism
Meanwhile, the newly-appointed US Homeland Security chief, Tom Ridge, has said fighting bioterrorism will be the main priority of the Bush administration in the coming weeks.
Interviewed by Mr Brokaw on America's NBC television network, Mr Ridge said there was not yet "credible evidence" to link the anthrax attacks to Saudi-born militant Osama Bin Laden, "but... we ought to operate under the presumption that it is".
He said the government was boosting its reserves of anthrax antibiotics and smallpox vaccine.
Earlier, FBI Director Robert Mueller said authorities had found no direct link with "organised terrorism" but had not ruled it out.
Hoaxers warned
The FBI says it has received more than 2,300 reports of suspected cases of anthrax since 1 October, including a spate of hoaxes.
US Attorney General John Ashcroft hit out at the perpetrators of phoney scares, warning culprits would be prosecuted.
"They create illegitimate alarm in a time of legitimate concern," he said.
In Florida, a 33-year-old Lee County Jail inmate faces up to 75 years in prison and a $50,000 fine after being charged with sending out letters claiming to contain anthrax spores.
Convicted robber Colin Perry is accused of writing five letters containing a white powdery substance and warning the recipients they were now infected by anthrax.
CNN reported that Frederick Forcellina allegedly threatened to use a weapon of mass destruction in three Connecticut towns.
Earlier on Tuesday Mr Ashcroft said that another man, Joseph Faryniarz, was charged with making false statements connected to a scare in the state's Department of Health and Protection.