The silent demonstration by 10,000 followers of the Falun Gong sect, which promotes meditation and martial arts, was the biggest in Beijing since the pro-democracy movement 10 years ago.
The media report quoted a government spokesman who said the protests were ''completely wrong'' but that people had a right to air grievances through legal channels.
BBC Beijing correspondent Duncan Hewitt says it is extremely rare for China to acknowledge any form of public protest, but analysts say the government appears anxious to calm tensions without alienating millions of the movement's followers.
The report, which was read on national television and ran on the front page in many newspapers, acknowledged both Sunday's protest and an earlier one in the city of Tianjin by Falun Gong followers.
It said it was wrong to surround central government headquarters as this would influence public order and added that anyone who exploited such movements to harm social stability would be dealt with according to the law.
However, it said it was permitted to hold different views and express them through legal channels and stressed that the government had taken a patient approach and never banned the Qi Gong exercises on which the movement is based.
Analysts say the reporting of the incident in itself is an acknowledgement of the strength of the movement's own communications network and appears designed to prevent the spread of rumours.
Discrimination
Protesters at Sunday's demonstration said they were angry at an article by a senior academic criticising Falun Gong.
Some said they were demanding the release of 40 or 50 people allegedly detained and beaten by police during the Tianjin protest.
The Chinese Government has now agreed to listen to the sect's grievances.
During the protest demonstrators sat or stood three or four deep for at least a kilometre along the streets opposite the State Council offices, beside the Forbidden City.
The Falun Gong teachings, influenced by Buddhism and Taoism, advocate Qi Gong exercises as a route to self-cultivation and benevolence.
They are thought to have millions of followers, many of them academics and officials. They say the movement is not a religion and have long complained of discrimination.
Country profiles
Falun Gong: A new cult emerges
(28 Apr 99 | Asia-Pacific)
Chinese fight for right to meditate
(26 Apr 99 | Asia-Pacific)
Tiananmen still haunts Chinese
(04 Jun 98 | Analysis)
Tiananmen 'tank man' still at large
(07 Apr 98 | Asia-Pacific)
Falun Gong - Introduction
Falun Gong - Web links
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