Qadri's brother Dilpazeer Awan, the only brother of six in the family who does not work for the government, said about 17 state investigation agencies were still questioning relatives on whether he had any ties to political or religious groups.
Awan said he believed Qadri acted on his own.
"If God is willing, even the government will support him when the time comes. We are hopeful that the judiciary will do justice," Awan told Reuters.
Even though Qadri confessed, analysts say the government is likely to tread cautiously because influential religious parties have succeeded in demonising Taseer, and those who opposed the killing have been silenced by fear.
"There is always the possibility that a lower court will rule against him, then there will be an appeal and there will be enormous pressure on the Supreme Court from lawyers and supporters to rule in his favour," said political analyst Riffat Hussein.
More than 500 lawyers have offered to defend Qadri for free.
Awan described his 25-year-old brother as an ordinary, dedicated member of an elite police force charged with fighting terrorism and protecting VIPs, not an extremist, as some police officials have said.
"He was a very caring, loving person. He was much better than all of us," said Awan, a property adviser and motor dealer in the Rawalpindi, also Qadri's home town.
A poster on a street outside his dingy office described Qadri as a ghazi. Qadri went to an English-language school, Awan said.
Qadri, father of a two-month-old boy, is in good spirits in prison, where he is being treated as a hero, said Tariq al Haqqani, who said he was one his lawyers.
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