Mr Taseer, one of Pakistan's most outspoken liberal politicians, was shot on Tuesday by a bodyguard angered by his opposition to blasphemy laws. Although many have condemned the assassination, some religious leaders have praised the governor's killer.
The governor - a senior member of the governing Pakistan People's Party (PPP) - had recently angered Islamists by appealing for a Christian woman, sentenced to death for blasphemy, to be pardoned.
Mr Gilani has declared three days of national mourning and appealed for calm.
The bodyguard, Malik Mumtaz Hussein Qadri, 26, was showered with rose petals by supporters as he appeared in court in Islamabad on Wednesday.
