The month-to-month decline in March was revised from 0.5 percent to 0.2 percent.
Export prices also fell in April, dropping 0.7 percent after a 0.5 percent decline in March.
The data for April is in line with expectations.
Fuel import prices fell for the second consecutive month, dropping 1.7 percent after falling 0.6 percent in March.
In the latest month, a 1.9 percent decline in petroleum prices "more than offset" a 6.1 percent increase in the price index for natural gas," the department said.
It was the first advance in natural gas prices since a 16.6 percent increase in the price in December 2012, the department said.
On an annual basis, the price of petroleum products was off 9.5 percent, which again "more than offset an 83.8 percent rise in natural gas prices," the Labor Department said.
Prices for non-fuel imports were down 0.2 percent in April. Non-fuel prices have dropped for two consecutive months.
For exports, prices fell 0.7 percent in April with agricultural export prices off 2.2 percent and non-agricultural export prices down 0.5 percent.