Conway and Beshear last week asked the judge for a delay in order to decide whether to appeal and/or to give themselves time to figure out how to implement the law.
The judge's decision was made official last week but was originally made two weeks prior -- the latest in a string of recent and significant legal rulings in several states on the subject of gay marriage.
While the judge's decision didn't legalize gay marriage in Kentucky, it is seen by activists as a significant step forward in a very red state.
The National Organization for Marriage praised Beshear's decision.
"He is doing what every elected official on every level of government across the country should do: defend the laws of the land," NOM president Brian Brown said in a statement.
Brown also criticized Conway in the statement, but gay marriage supporters and liberals praised Conway, who is seen as a potential candidate for governor in 2015.
Rep. John Yarmuth (D-Ky.) was among them.
"Today, Attorney General Conway made a courageous decision to stand up for equality in Kentucky and against a discriminatory law. He gave this case the thorough analysis it required, and his conclusion will place him and our Commonwealth on the right side of history," Yarmuth said.
U.S. Attorney General Eric Holder recently encouraged state attorneys general not to defend gay marriage bans if they discriminated in an unconstitutional manner.
This post has been updated.