Kenyatta and Vice President William Ruto were indicted by the International Criminal Court for allegedly playing a role in the post-election violence that left more than 1,000 Kenyans dead in 2007. Kenyatta bested challenger Raila Odinga in elections this year. Odinga's challenge to election results in 2007 sparked the violence.
A face-to-face survey of 2,000 Kenyan adults conducted by polling company Ipsos Synovate found the population split evenly on Kenyatta's war crimes trial.
On the ICC issue, 39 percent of the respondents told pollsters they wanted Kenyatta's case to stay at The Hague, 32 percent said they wanted the case tried in Kenya, and 29 percent said the charges should be dismissed.
Both men deny inciting the violence. Kenyatta said he expected the case to be dropped because of similar ICC rulings on the Kenyan violence. A trial date was set for Kenyatta for later this year.
Ipsos Synovate found 54 percent of the Kenyans taking part in the survey said the high cost of living was their main national concern. The polling company said 49 percent of those asked for their opinion said their economic outlook was poor.
The company said the margin of error for the poll was plus or minus 2.2 percentage points.