The call between the foreign ministers came as a surprise as Vietnam had refrained from publicly lobbying for her release until Tuesday.
Huong is set to appear in court on Thursday after her lawyers asked the attorney-general to withdraw her murder charge. Prosecutors may decide then inform the court whether the application is successful.
Authorities believe that North Korean agents recruited Huong, who hails from Vietnam, while she worked at a bar in Hanoi.
"So, there's a process following rule of law and there's a law to drop the charges, that's what happened".
Siti Aisyah and Huong have maintained that they believed they had been hired to participate in a reality TV prank show.
The two women allegedly assaulted Kim Jong-Nam - half brother of Kim Jong-un - on February 13, 2017, at Kuala Lumpur airport, in an action that Seoul attributed to North Korean agents and which was captured on security cameras. Pyongyang has denied the accusation.
Her lawyers have now asked that her case be adjourned and charges against her be dropped, too. Siti said she was happy to meet Jokowi. They have gone through the proceedings and the charge was being withdrawn, so this is being done according to the law.
Huong's lawyers had written twice to former AG Mohamed Apandi Ali to stop the prosecution but were unsuccessful.
Analysts say Malaysia risks creating a rift with Vietnam if it doesn't do the same for Huong.
"We have lined up four to five defence witnesses should there be no favourable reply from the AG", he said.
Yesterday, deputy public prosecutor Iskandar Ahmad did not provide a reason for the withdrawal of the charges against Siti Aisyah.
Salim said Huong should also be accorded the same treatment although both were charged separately, but a joint trial was held.
"I have no information (regarding that)", he said, when quizzed by the media during a press conference in Parliament Tuesday (March 12).
Analysts said Aisyah's release was in part due to politics and the improved relations between Indonesia and Malaysia that have come since Mahathir Mohamad returned to the Malaysian premiership past year after the stunning election defeat of Najib Razak.
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