The United Wa State Army (UWSA) stopped fighting the government in 1989 in exchange for control of a remote portion of territory bordering China which is believed to be awash with drugs.
But they have a 20-25,000-strong standing army and are yet to commit to a full nationwide ceasefire, undercutting Suu Kyi's aim of swiftly securing a lasting peace.
Several complex ethic conflicts are rumbling across Myanmar's borderlands, hampering efforts to build the country's economy after the end of junta rule.
The Wa are accused of producing and trafficking huge amounts of methamphetamine and heroin from their secretive holdout and buying weapons with the proceeds.
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Today's "very positive discussions" between leaders of the Wa, a powerful group called the Mongla army, and Suu Kyi were an "important first step" in building trust, Zaw Htay, spokesman for her office, told reporters.
Suu Kyi wants to convene a meeting to thrash out the precepts of greater federal autonomy for ethnic groups in exchange for peace.
But that deal collapsed under the junta that took control several years after Aung San's assassination and embarked on almost 50 years of devastating rule.
Suu Kyi has not set a date for the meeting but is ramping up efforts to ensure all rebel groups are at the table.
Both the USWA and Mongla army "support the 21st century Panglong conference and they will try to participate", Zaw Htay added.
Tens of thousands of people have been killed or displaced by the decades of war.