Mr Ashcroft made his call on television
Mr Ashcroft said preventing terrorism should be the number one priority of American laws and that some parts of current legislation made it easier to fight organised crime than terrorism.
The BBC's Jon Leyne in Camp David says that the measures are the first tangible signs of the way US society and law may be changed by Tuesday's attacks.
He says that they are bound to provoke unease among defenders of civil liberties.
Mr Ashcroft said that he would ask Congress to allow specific individuals to be targeted for surveillance rather than just specific telephones.
The spread of mobile and even disposable phones made the move necessary, he said.
And he said that he wanted the penalties for harbouring or assisting terrorism to be brought in line with those for espionage.
E-mail trawl
Mr Ashcroft's comments follow moves by the FBI to scour e-mail traffic for clues as to who might have been behind the terror attacks on New York City and Washington.
Two major US internet service providers confirmed on Friday that they were co-operating with the investigation.
But privacy advocates are concerned the authorities may stampede over digital civil liberties in their zeal to catch the attackers and prevent possible future terrorist strikes.
The FBI has shied from providing details about its investigation, and would not say whether its controversial Carnivore e-mail monitoring program was involved.
'Relevant and helpful'
The two ISPs concerned, AOL and EarthLink, confirmed they were assisting authorities with information from their user and connection logs.
Earthlink said the company had received similar subpoenas from the federal government.
"We're co-operating, but we're not installing any surveillance equipment on our networks," said an Earthlink spokesperson.
Routine destruction
And in the UK, the authorities have asked phone companies and ISPs to keep records of all communications on the day of the attacks.
The National Hi-Tech Crime Unit, set up earlier this year to fight crime related to information technology, said data stored might hold vital evidence about those responsible for the violence.
Police said they were not looking for anything in particular but made the request as text message, e-mail and voice message logs were routinely destroyed after 48 hours.
Last year, the FBI was heavily criticised when it revealed it had installed Carnivore devices at several ISPs.
Carnivore criticised
Carnivore, now also called DCS1000, records all the electronic communications of a suspect.
But privacy advocates fear the software could lead to random surveillance of e-mail messages unrelated to an FBI investigation.
"There will be a lot of data-collecting cloaked in national security concern," said Lori Fena, chairwoman of Truste, a non-profit organisation concerned about online privacy.
Experts said it was unclear how useful an ISP's records would be to the investigation, particularly because of the amount of information involved.
Mass of information
AOL membership recently surpassed 31 million accounts, and EarthLink has about 5 million subscribers.
"Once you have the e-mail, you can look at all the other information in it, including the entire route," said Brian O'Higgins, of security internet firm Entrust.
But the ability to find relevant information may depend on the techniques used by potential suspects.
It is possible to communicate across the internet in a secure manner, encrypting crucial information.