
Aung San Suu Kyi, together with two companions and an American John Yettaw - who swam across the Inya lake to her residence - are being tried in a special court in the notorious Insein prison for the second day.
If the court convicts Suu Kyi, she would face five years' imprisonment, an automatic extension of the term in detention she received in 2003.
The international community has expressed concern over the case and the US has renewed its sanctions against the junta.
Senior officials of Asean met Monday and yesterday in Phuket to seek a common stance, but a concrete solution cannot be expected, say observers.
The latest statement by Prime Minister Abhisit also expressed grave concern for Aung San Suu Kyi's situation, given her fragile health, and called on the junta to provide timely and adequate medical care for her.
Burma, as a responsible member of Asean, has the responsibility to protect and promote human rights, the statement said.
With the eyes of the international community on Burma, the honour and credibility of its government are at stake, it said.
"We hope Myanmar will listen to other Asean colleagues and ... Asean is ready to contribute constructively to the national reconciliation process and the peaceful transition to democracy," Prime Minister Abhisit said.
However the regional grouping and neighbouring Thailand would not take any tough action or set a deadline for the junta to comply, he said.