Assad, facing intensifying protests against his 11 years in power, had earlier pledged to replace the emergency law with anti-terrorism legislation but opposition figures said this was likely to preserve draconian curbs on freedom of speech and assembly in Syria, under monolithic Baath party rule since 1963.
"Next week is the maximum (time) limit for completion of these laws regarding the lifting of the state of emergency," Assad said in a speech to a new cabinet he named last week, broadcast by Syrian state television.
"When the lifting of the emergency law package is issued, it should be firmly enforced. The Syrian people are civilised. They love order and they do not accept chaos and mob rule," he said.
"We will not be lenient toward sabotage," Assad said in a speech to a new cabinet he named last week.
The 45-year president did not mention the main demands of tens of thousands of protesters to end the tight grip of security services on everyday life, release thousands of long serving political prisoners, most of whom have been held without trial, and do away with a clause in Syria's constitution that enshrines the Baath Party as "leader of the state and society".
Assad said corruption was a problem but he announced no measures to curb his own family's dominance over the Syrian economy. His cousin Rami Makhlouf, a tycoon, has expanded his businesses during Assad's rule and he has been widely named by protesters in their calls for an end to public corruption.
Assad said stability remained his priority but that reform was needed to "strengthen the internal front", following unprecedented protests against his authoritarian rule over the past month.
"We do not want to be hasty. Any reforms have to be based on maintaining internal stability," Assad said.
His use of force and mass arrests, mixed with promises of reform and concessions to minority groups and conservative Muslims, have not placated protesters inspired by popular uprisings which toppled leaders in Tunisia and Egypt.
He unveiled the new government on Thursday and ordered the release of some detainees, but the government has little power in a one-party state dominated by Assad, his family and the security apparatus.
Demonstrations swept into the capital Damascus on Friday for the first time and thousands of protesters marched elsewhere.
Thousands of people also protested in the southern city of Deraa, the fount of the protest wave, on Saturday chanting: "The people want the overthrow of the regime", two witnesses said.