At least 10 people died and thousands were arrested when troops used force to end peaceful anti-government marches.
Burma's leaders have now appointed a go-between for opposition talks.
An official had been charged with liaising with detained pro-democracy leader Aung San Suu Kyi, state media reported on Monday.
Ms Suu Kyi's party, the National League for Democracy, welcomed the appointment, saying: "Finding a solution through dialogue is the natural way to help the people and the country."
The party won a landslide election victory in 1990, but the ruling generals have never allowed them to govern.
Correspondents say the move, recommended by UN special envoy Ibrahim Gambari when he visited the country last week, seems to be a concession to international pressure.
Countries including the US, UK and France are campaigning for sanctions against the regime, but Burma's neighbours oppose such action.
On Tuesday, China's foreign ministry reiterated its position, saying "sanctions or pressure will not help to solve the issue".
The government's crackdown has seen curfews imposed in Burma's main cities, and frequent night-time raids on monasteries and private homes.
Ye Min Tun, who describes himself as a "good Buddhist", sent a letter of resignation to the Burmese embassy in London.
In an interview with the BBC, he described the crackdown on the September protesters as "horrible".
"I have never seen such a scenario in the whole of my life. The government is arresting and beating the peaceful Buddhist monks."
He said he had hoped that the protests would force the generals to come to an agreement with the opposition.
"This revolution, this incident seemed to be the decisive factor that could persuade the government to go to the negotiation table.
"But actually the government ignored the reality," he said.