Mexican President Vicente Fox has said his government has failed to defeat violent crime, after a protest in Mexico City by over 250,000 people.
The protesters paid tribute to crime victims
Mr Fox, who has proposed reforms to the judiciary, said greater efforts were needed to tackle kidnapping, mugging, car-jacking and murder.
Demonstrators marched silently through the Mexican capital at the weekend, paying tribute to crime victims.
Kidnappings are rife in the city and many abductions go unreported.
Correspondents say people lack faith in the justice system.
Mexico has the second-highest number of kidnappings in the world, with some 3,000 reported cases last year.
'More to do'
Mr Fox said the protesters were right to criticise the government for its failures.
"Society has spoken and we have listened to its dissatisfaction and anger," he said.
"Our society was right - governments have only reached partial solutions in the struggle against crime and we still have much more to do."
He called for harsher punishments, but said the priority was for the authorities to become more efficient in hunting down criminals.
But the president's main political rival, Mexico City mayor Andrés Manuel López Obrador, said the government was manipulating the issue and had sought to blame him for the high crime figures in the capital.
"I continue to think they were stirring things up... to manipulate this issue," he said.
Mr López Obrador wants to stand for president in 2006.
Colours of mourning
The non-political march - hailed as the largest in the capital's history - was called by more than 80 non-governmental organisations and groups.
Most of the people were wearing white clothes, responding to organisers' calls before the rally.
Participants filled the capital's central square and adjacent streets.
Instead of chanting, many demonstrators shared stories about how they had been victims of violent crime.
They later pinned black ribbons to their white clothes in memory of crime victims.