Cooke's comments came two days after national Democrats voted to include language in the party's platform that calls for recognition of same-sex marriages and defense of legal abortions.
Cooke said he opposes abortion except in cases of rape, incest or to save the life of the mother the same position as the LDS church.
Cooke said he wanted to make his positions clear on the polarizing issues, so he and Gov. Gary Herbert can have a substantive debate on the issues he believes Utahns care about funding education, fostering good-paying jobs, protecting Hill Air Force Base and showing leadership in state government.
Despite his differences with the national Democratic Party, Cooke said he will be voting for President Barack Obama over Republican nominee Mitt Romney, although he said that he could work with either as governor.
And he supports allowing same-sex couples the right to adopt children a practice that is banned under current state law.
The Herbert campaign had a restrained response, noting there is little distinction between the candidates on the issue.
"The governor has made his support for traditional marriage and families very clear," said spokesman Marty Carpenter.
Brandie Balken, executive director of the group Equality Utah, a group that advocates for lesbian, gay, bisexual and transgender rights and has endorsed Cooke, said that the group disagrees with Cooke on the marriage issue. But he supports their push for non-discrimination laws and anti-bullying laws, and other efforts and they will continue to support him.
"I think it's fair to say his policy position on [gay marriage] is in line with the majority of Utahns," and the conversation will continue, she said.
Weston Clark, a delegate to the Democratic National Convention who is raising a son with his partner, said it is unfortunate that there is a disconnect between the views of politicians and citizens of the state.
"I think he was wrong on this one and it is out of step with the values of Utah," said Clark. "I support Peter Cooke. I would vote for Peter Cooke and he's right on 99 percent of the issues, but there definitely needs to be some education here."
A poll in February by the Center for the Study of Elections and Democracy at Brigham Young University found that 43 percent of Utahns support recognition of civil unions and another 28 percent support legalizing gay marriages. Just 29 percent opposed any recognition of same-sex relationships a level of opposition that has shrunk significantly over the years.
Just 3 percent of Democrats oppose any recognition for gay couples, compared to 42 percent of Republicans and 18 percent of independents.
Quin Monson, director of the BYU center, said Democrats running statewide still have to try to win over Republican voters and typically that has meant distancing themselves from the national party. That may not be as true as it once was, he said, but having the same stance as Herbert essentially nullifies the issue.
"He's in a very, very small group of Democrats who favor no legal recognition [for gay couples], but [Democrats] are not who he needs to win the election," Monson said. "Maybe his issue position here isn't concocted to appeal to voters. Maybe this is what he really thinks."
Clark said he was grateful that Cooke supports adoptions by same-sex couples, but if it is acceptable for gay couples to adopt a child, they should also be able to get married, if nothing else for the protection of the child if something were to happen to either partner.
"It seems like if you're going to be OK with entrusting a child to me and my partner, marriage should just be a given," he said.