The trial is taking place against a backdrop of mounting international criticism, with the US state department calling the charges "unjustified" and France labelling the trial a "scandalous provocation".
The latest charges stem from an incident in which John Yettaw, a US citizen, was arrested after allegedly swimming across a lake to secretly enter her home.
|John Yettaw is also on trial with Aung San Suu Kyi in Yangon's Insein prison [EPA]
According to police he stayed there for two days before trying to swim back.
Yettaw, 53, is also facing charges related to the case along with two female aides of Aung San Suu Kyi.
Ian Kelly, the US State Department spokesman told a news briefing in Washington on Monday that an American consular officer present had been present in the courtroom on Monday during the first day of proceedings.
"Mr Yettaw faces charges relating to immigration, trespassing into a restricted zone, and violating a law that protects the state from those desiring to cause subversive acts," Kelly said.
The trial has been condemned by the US and European Union, as well as the Association of Southeast Asian Nations (Asean), a regional which includes Myanmar but which usually avoids direct criticism of its members.
On Tuesday Thailand, which currently chairs the regional group, expressed "grave concern", saying that Myanmar as a "responsible" Asean member "has the responsibility to protect and promote human rights".
It also warned that with growing international criticism "the honour and credibility" of the Myanmar government was at stake.
However, the statement ruled out Asean sanctions against Myanmar.
On Monday the European Union said it was considering tougher sanctions against Myanmar, although Carl Bildt, the Swedish foreign minister, said that there was little more that the EU itself could add to existing measures.
"Our problem with sanctions on Burma is that we have sanctions over virtually everything relevant for the European Union," he said, using the former name for Myanmar.
"Our relationship with Burma is nearly non-existent and that makes it complicated from this point of view, but we'll have to engage with the other countries in the region, those are the ones who have a real possibility of influence."
The hurriedly arranged trial comes just days after Aung San Suu Kyi was taken from her lakeside property and imprisoned at what the government calls a "guest house" inside the Insein prison compound.
|The trial is being held behind closed doors inside Yangon's Insein prison [AFP]
"She just felt sorry for this man [Yettaw] as he had leg cramps after he swam across the lake. That's why she allowed him to stay," said Kyi Win, a lawyer representing Aung San Suu Kyi.
According to the official police complaint against her, she is charged under Myanmar's laws on "Safeguarding the State from the Dangers of the Subversive Elements".
Nyan Win, a spokesman for Aung San Suu Kyi's National League for Democracy Party (NLD) has said he expects the trial to last up to three months.
As the trial was set to resume on Tuesday around 200 NLD supporters gathered outside the jail.
They were countered by a large group of supporters of Myanmar's military government, although there were no reports of clashes between the two groups.
Aung San Suu Kyi had been scheduled to be freed on 27 May after six consecutive years of house arrest, but opposition groups have said they expected the military government would try to find reason to continue to hold her, as has happened in the past.
The military government, headed by Senior General Than Shwe, has kept the opposition leader in detention for a total of 13 years since 1990, when it refused to recognise her party's landslide victory in Myanmar's last elections.
The military has ruled Myanmar since 1962.
Critics say the new charges are a pretext for the government to keep Aung San Suu Kyi out of new national elections scheduled for next spring.
The government has labelled the vote the culmination of Myanmar's "roadmap to democracy," but opposition groups say it is attempt to legitimise continued military control.