The ruling party lawmakers proposed the children's agency last week in an effort to woo voters ahead of a general election, reports Xinhua news agency.
"We need to eliminate the sectionalism of policies and consider how an organisation should be," Suga said during a meeting of the House of Councillors' Audit Committee on Monday.
"From the broad standpoint of ensuring Japan's future, I want my party to study the establishment of such an agency," he said.
The Liberal Democratic Party (LDP) lawmakers asked the government to set up the agency to coordinate child policies in terms of medical and educational services and those handled by police as part of the country's efforts to address its low birth-rate.
Suga has already instructed the LDP to produce a blueprint for the agency, according to local media reports.
It will be set up as part of a special organisation under the Prime Minister and headed by Secretary General Toshihiro Nikai.
In order to appeal to people with children, the government is trying to include the children's agency in its basic policies to be compiled around June.
The agency may be in charge of issues including child poverty, abuse and suicides as well as the realignment of the administrative jurisdiction of nursery schools and kindergartens.