The Tory MP, who last week voted against Government plans to introduce gay marriage, made his remarks to ITV Wales's Face To Face programme.
Shadow Welsh secretary Owen Smith blasted the comments as evidence that the "nasty party is alive and well under David Cameron".
Mr Jones said: "I regard marriage as an institution that has developed over many centuries, essentially for the provision of a warm and safe environment for the upbringing of children, which is clearly something that two same-sex partners can't do.
"Which is not to say I'm in any sense opposed to committed same-sex partnerships."
Mr Jones said he did not believe he was homophobic, insisting he had "people in my life who are important to me who are gay".
The Welsh Secretary said he took the chance of a free vote to oppose the plan, which he said he believed his constituents opposed.
But Mr Smith said: "These comments reveal that the nasty party is alive and well under David Cameron. David Jones's comments are offensive and he should apologise immediately."