Reports say Indonesia is now the biggest terrorist threat
The deal is a toned-down version of proposals by President George W Bush.
The bill is expected to be introduced to the House on Tuesday and approved by the Judiciary Committee on Wednesday.
The package, proposed by the top Republican and Democrat members on the Judiciary Committee, gives law enforcers more power to:
Reuters news agency said it had obtained a copy of the bill which showed that the proposals also ruled out President Bush's provisions which were opposed by civil liberty groups.
These include:
The initial proposals by President Bush and Attorney General John Ashcroft were issued in response to the devastating attacks on New York and Washington on 11 September.
On Sunday Mr Ashcroft warned Americans of the likelihood of "further terrorist activity" in response to prospective US military action in Afghanistan, and called on Congress to act quickly.
New anti-terrorism laws, he said, would make it easier to conduct searches and detain immigrants.
Mr Ashcroft wants both the House of Representatives and the Senate to pass legislation by the end of the week and send it to President Bush to sign into law.
But Senate Judiciary Committee Chairman Patrick Leahy has not yet even scheduled a hearing on a pending Senate version of the bill, Reuters reported.
President George W Bush spent Sunday meeting key advisers at his Camp David presidential retreat, to consider further the US response to the attacks.
The FBI says it is following up more than 100,000 leads, which it hopes will lead to more information about them.
Hostage threat
Mr Ashcroft's statements follow the warning by the US State Department on Friday that Islamic extremists may be planning to kill or kidnap American and British civilians in the event of American retaliatory action.
The State Department issued the statement after warnings from foreign and US intelligence agents.
US press reports have indicated that the most serious reported threat is in Indonesia, where radical Muslim groups reportedly plan to invade the wealthy neighbourhoods of Jakarta and seize large numbers of potential hostages should strikes against Afghanistan be carried out.
There have also reportedly been threats in Pakistan, Tajikistan, Uzbekistan, Malaysia, the Philippines, Bangladesh, Georgia and Bahrain.
Travellers have also been urged to be particularly careful in Muslim nations or those with large Muslim populations.