At a news conference at the embassy, Indonesian Minister for Law and Human Rights Laoly said that his office had written to Malaysian Attorney General Tommy Thomas to reconsider the charges against Aisyah.
"She is entitled to the same kind of consideration as Aisyah", he said.
"I finished my job", she said.
It was not immediately clear why Aisyah was released and not Huong, but Indonesia often makes concerted diplomatic efforts to get its citizens on death row overseas released.
"You may be lonely now, quietly longing for freedom. May God continue to protect us".
"I had wanted to see my family for a long time".
"We are investigating this incident at all angles including it being the work of mischievous youths", he said.
Yasonna added that Jokowi had personally requested Mahathir to release Siti during the Malaysian premier's visit to the Bogor Palace in West Java past year.
"We've heard the news and we're so happy". He speculated that the prosecution had determined that it could not prove the charges against his client. "Woman charged with Kim Jong Nam's killing freed in shock ruling".
Malaysia agreed to Indonesia's request to drop charges against an Indonesian woman accused in the 2017 killing of the North Korean leader's half-brother, its attorney general said in a letter on March 8.
Huong remains on trial at the court in Shah Alam and is set to give her first testimony in the coming days.
Gooi Soon Seng, Siti Aisyah's lawyer, said his client was "a scapegoat".
Doan's lawyer, Hisyam Teh Poh Teik, added that he is applying for full acquittal and that his client was traumatised by the court's decision to only free Siti.
Hundreds of local media personnel had been awaiting her arrival from 3 pm, the decision by Justice Datuk Azmi Ariffin on the case was being widely broadcast.
Prosecutor Iskandar Ahmad said Aisyah's discharge without an acquittal means she can be charged again if there is fresh evidence, but that there are no such plans now.
It said Aisyah, a migrant worker, never had any intention of killing Kim. "I did not expect it", said the 27-year-old, who was wearing a red headscarf.
The case against Huong will take a major step forward Monday, when she is expected to testify.
In a statement posted on its website, the group appeared to have acted in support of the two women defendants.
The women, in their 20s, had always denied murder, saying they believed they were taking part in a prank and were tricked by North Korean agents into carrying out the Cold War-style hit using VX nerve agent.