Until now, General Shwe has refused to answer Ban's calls or letters, and in the past has also snubbed Ibrahim Gambari, Ban's special envoy to Burma.
Shwe made his first public appearance early this week, more than two weeks after cyclone Nargis flooded a region that is home to an estimated 3.5 million people and 30 percent of Burma's rice production.
Pressure from Burmese leaders?
"There's tremendous pressure from within his own group," says Josef Silverstein, professor emeritus of political science at Rutgers University in New Jersey. "There are senior officers who may be quietly trying to get him to open up in certain ways. These men are not idiots. They have radio and TV. They know what's going on.
"They have this delusion of grandeur, and they are being called all kinds of names, people with no heart or sympathy," he continues. "I believe there's an internal pressure in the ruling group. More importantly, I think they're getting pressure from China. China has quietly been trying to act as intermediaries to get them to open up."