Links to the church, founded in South Korea in the 1950s and famous for its mass weddings, have become a headache for Kishida since July 8, when former premier Shinzo Abe was shot.
Abe's suspected killer said his mother was bankrupted by the church and blamed the former prime minister for promoting it.
According to a survey taken at the weekend by the Mainichi Shimbun newspaper, Kishida's support fell to 36 per cent from 52 per cent a month ago - its lowest since he took office last October.
Those who believed ties between the Unification Church and Kishida's ruling Liberal Democratic Party (LDP) were either "an extreme problem" or "something of a problem" hit 87 per cent.
Only four per cent believed it was not a problem at all.
Kishida reshuffled his cabinet on August 10 and removed some cabinet members with ties to the church in an attempt to bolster support but 68 per cent of respondents said they did not approve of the move, against only 16 per cent who did.
Meanwhile, new COVID-19 cases remain persistently high, prompting 55 per cent of respondents to say they did not approve of the government's handling of the situation.
On Sunday, Kishida himself tested positive for the virus, forcing him to cancel a trip to an aid conference in Tunisia.
On the question of the state funeral for Abe - set for September 27 and to be paid for by the government - 53 per cent said they were against the idea.
