He made the comments in a televised speech to his newly formed cabinet.
The lifting of the 48-year-old emergency law has been a key demand of the protesters.
On Friday, tens of thousands of demonstrators rallied in the capital, Damascus, in one of the biggest turnouts since protests began.
While he repeated his view that his country was facing a conspiracy, Mr Assad said he did not believe the lifting of the state of emergency would destabilise Syria.
The Syrian leader told the cabinet a legal commission asked to examine the lifting of the law had come to its conclusions.
"I think the commission has finished its work, on Thursday, and the recommendations will be given to the government so that they become law immediately. I don't know how many days it will take you and I think that the maximum deadline for the lifting of the state of emergency will be next week," he said.
The law bans public gatherings of more than five people.Continue reading the main story Owen Bennett Jones BBC News, Beirut
This is new language, but it's only language at this point. It sounds like the emergency law will be lifted - that's a very clear commitment President Assad has made - but it has taken quite a long time to get here.
So when you think of much more far-reaching measures, like multi-party democracy - which, as he said, would completely transform the political situation in Syria - then surely that is going to be a much more difficult pill for the regime to swallow.
And you would imagine that while he is asking the government to study the proposal, it is the sort of thing that would be extremely difficult for them to do.
The question now is whether the protesters think they've achieved something by getting rid of the emergency law and head home, or whether they see that their time on the streets has forced this change from the government, and decide to stay on the streets to get more.New security legislation would be introduced in place of the emergency law, he said, adding that the new government should also study ideas for a multi-party system and greater press freedom.
The question now is whether the measures will be enough to persuade the demonstrators to go back to their homes, says the BBC's Owen Bennett Jones in neighbouring Lebanon, or whether they will simply encourage more protests in the hope of securing more reforms.Batons and tear gas
Friday's protests in Damascus and other cities were among the largest in a month of unrest that has reportedly seen some 200 people killed.
The unrest is the biggest challenge to the rule of Mr Assad, who inherited power from his father in 2000.
Security forces used tear gas and batons to disperse tens of thousands of protesters - some calling for reform, others calling demanding the overthrow of Mr Assad - in Damascus.
Thousands of people reportedly demonstrated in a number of other Syrian cities - including Deraa, Latakia, Baniyas and Qamishli - where violence has been previously reported.
Mr Assad formed a new government on Thursday and pronounced amnesty for an undisclosed number of people detained in the last month.
He has also sacked some local officials and granted Syrian citizenship to thousands of the country's Kurdish minority - satisfying a long-held demand.
The United Nations and a number of Western governments have decried President Assad's use of force to try to quash the protests.
Human rights campaigners say hundreds of people across Syria have been arrested, including opposition figures, bloggers and activists.
Mr Assad blames the violence in recent weeks on armed gangs rather than reform-seekers and has vowed to put down further unrest.
US officials have said Iran is helping Syria to crack down on the protests, a charge both Tehran and Damascus have denied.
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