The attack was soon claimed by the outlawed Baloch Liberation Army (BLA) which said it would not tolerate "any Chinese military expansionist endeavours on Baloch soil".
A Pakistani father and his son, two police officers, and the attackers were killed.
China "strongly condemned" the attack and asked Pakistan to take measures to ensure the safety of Chinese citizens and institutions in the country, as well as the China-Pakistan Economic Corridor (CPEC) megaproject.
In addition to the exchange of gunfire, eyewitnesses told Pakistan's Dawn news channel that they heard an explosion.
Pakistani Prime Minister Imran Khan ordered an inquiry into the attack, calling it a "conspiracy" against the strategic cooperation between China and Pakistan.
The sources said that Achchu is one of the key commanders of BLA chief Dr Allah Nazar.
Around three to four terrorists reached the area and started firing and hurled a couple of hand grenades at the police personnel deployed for security in the area.More news: Sidhu expresses gratitude to PM Imran for opening Kartarpur border
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The Balochistan Liberation Army, a Pakistani insurgent group, claimed responsibility for the attack, which occurred about 9:30 a.m. local time.
He added that the group "ran away" but did not confirm if the attack was over, saying the area had been cordoned off and security forces were conducting a clearing operation.
Separatist militants who oppose Chinese investment projects in western Pakistan say they carried out the attack. Resident there allege that the Chinese-led expansion of the port has stripped Baloch fishermen of their livelihoods, pushed them out of the homes and siphoned off their water supply.
China has poured billions into Pakistan, and thousands of Chinese nationals visit the country to work on CPEC projects or other business ventures.
A spokesman for the BLA confirmed there were three attackers. Authorities said most of the victims were minority Shiite Muslims. Beijing is investing tens of billions of dollars in the country in what is known as the China-Pakistan Economic Corridor or CPEC.
No militant group has claimed responsibility for the blast, but Orakzai has been the scene of militant attacks in recent years, mostly claimed by Pakistani Sunni militants.
Pakistani students protest to condemn a bombing in northwest Pakistan's Orakzai region that killed at least 25 on Friday.
They said Achu had fled after getting injured in an encounter with the Pakistani security forces 18 months ago. China is also a close financial and political ally of Pakistan.
The assault on the consulate is particularly significant because it took place in Karachi, the commercial capital of Pakistan, rather than in the remote province where the militants are based.