There were no immediate claims of responsibility for the December 28 attack, but a Taliban spokesman denied that the militant group was involved.
The UK and the U.S. also condemned the attacks, which killed at least 41 people and injured many more.
"The Malaysian government also expresses its deepest condolences and sympathies to the Government of the Islamic Republic of Afghanistan and the families of the victims", the statement said.
The Afghan Voice news agency housed on the second floor of the building was also hit.
According to the Philippine Department of Foreign Affairs, none of the estimated 1,500 Filipinos working in Kabul and other parts of Afghanistan were among the casualties in the attack.
"A ceremony was being held to mark the 38th anniversary of the Soviet invasion in Afghanistan when the explosion went off".
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Taliban forces fighting US-led North Atlantic Treaty Organisation forces in Afghanistan have denied any involvement in the attack.
The Middle Eastern jihadist group has gained ground in Afghanistan since it first appeared in the region in 2015 and has scaled up its attacks in Kabul, including on security installations and the country's Shiite minority.
The attacks have increased pressure on President Ashraf Ghani's Western-backed government to improve security.
"This is not the first and this won't be the last", a mullah overseeing the burial told the mourners, warning of more attacks in the country. In a statement to Tolo News, the man said he doesn't know the number of casualties and that he fled the moment he heard the explosion. "In one of the deadliest years on record, journalists and other civilians continue to be ruthlessly targeted by armed groups".
According to the Interior Ministry, the explosion at the Shia center was followed by at least two more blasts.
According to a report this month by media freedom group Reporters without Borders, Afghanistan is among the world's most risky countries for media workers with two journalists and five media assistants killed doing their jobs in 2017, before Thursday's attack.