Hong Kong's leader, Tung Chee-hwa, has said a controversial anti-subversion bill will be amended, following a huge protest rally earlier this week.
Protesters feared the new law would curb their freedoms
Pressure has been mounting for Mr Tung to address citizens' concerns over the bill - known as Article 23 - since 500,000 people marched through the territory's streets on Tuesday.
Religious groups, human rights organisations and journalists say the bill would give the government power to suppress their activities.
The authorities in Beijing have said they approve of Mr Tung's changes. But his critics say the concessions do not go far enough.
On Saturday Mr Tung said he would
He also wants to modify provisions that would allow organisations linked to outlawed groups in the mainland to be banned in Hong Kong.
provision that allowed some groups to be banned
add protections for journalists who publish classified information
delete a provision that would let police conduct searches without warrants.
This could involve the Falun Gong spiritual group, which is legal in Hong Kong but has been banned in China as an "evil
Mr Tung acknowledged that the massive outpouring of public sentiment had forced an embarrassing retreat from parts of the national security law and said "my colleagues and myself have to do better".
"After repeated and detailed discussions, we have decided to make amendments to further allay people's fears," Mr Tung told
a news conference.
Article 23 is part of Hong Kong's mini-constitution - the Basic Law - which was negotiated on its handover from Britain to China in 1997.
The amended bill will be submitted to Hong Kong's legislative council for a final vote on Wednesday.
The BBC's Francis Markus, in Shanghai, says Mr Tung has been in the throes of political crisis over the last few days and now seems to have decided that something had to give.
The law has not been the only focus of widespread public discontent - there has been widespread criticism of the government's handling of various issues.
Our correspondent says the debate over the bill was likely to be stormy but even if the amendments allowed the bill to pass, critics were likely to sense Mr Tung's increasing weakness and continue pressing their calls for him to step down.