Mr Cameron was accompanied by Welsh Secretary Cheryl Gillan as he visited a local business and the Welsh Assembly.
The Prime Minister was shown around a jet engine maintenance facility near Cardiff run by GE Aviation and held a question and answer session with workers.
He then travelled to the Assembly’s Senedd building in Cardiff Bay where he spoke about the relationship between central Government and the devolved Welsh government.
The PM said:
I wanted to come to Wales in my first week of being Prime Minister to show the respect that I have for devolution and trying to make sure that we make devolution work even better in the future. The respect agenda to me really means something. I want there to be respect between the Welsh Assembly and the Westminster Parliament.
During the visit, the PM also held meetings with the Assembly’s Presiding Officer Lord Elis-Thomas and First Minister Carwyn Jones.
It follows the PM’s visit to Edinburgh last week, when he went to the Scottish Parliament and held talks with First Minister Alex Salmond.