In Suu Kyi`s first-ever meeting with the leader of a foreign country, the pair`s half-hour talks in Yangon on Tuesday were held in a "good atmosphere", Titima Chaisang, chief Thai government spokeswoman, told AFP.
"Aung San Suu Kyi told Prime Minister Yingluck that she hopes to win in the by-election and Yingluck offered her support and her hope that Aung San Suu Kyi will win," she said.
No polling date has been set for the election, which will see Suu Kyi run for office for the first time. She was under house arrest when her opposition party won a 1990 poll, but the military regime did not allow it to take power.
Detained for most of the past two decades, Suu Kyi was freed from her latest house arrest term a few days after a rare election in November last year, which her opposition party boycotted saying the rules were unfair.
The government this month allowed the party to rejoin mainstream politics and granted Suu Kyi various high-profile meetings, including with US Secretary of State Hillary Clinton and China`s ambassador to Myanmar.
Thailand and Myanmar are key partners and Yingluck expressed support for her neighbour`s "path of national reconciliation", adding that its progress was good for the Association of Southeast Asian Nations, of which both are members.
"We have seen the good intentions of Myanmar`s government to open up and to embark on democratic development," she told reporters back in Bangkok on Wednesday, adding that future developments should be monitored.
The Thai premier`s comments echoed others from the international community that have welcomed a number of reformist steps by Myanmar`s quasi-civilian government this year.
Yingluck, who spent two days in Myanmar, first travelled to the capital Naypyidaw on Monday for a meeting of Greater Mekong country leaders, where she said the talks "progressed well".
She took office in August after sweeping to an election victory with the support of her older brother, fugitive former premier Thaksin Shinawatra, who was deposed in a 2006 coup.