Assembly Speaker Sheldon Silver is still holding out hope for a faster increase in the state’s minimum wage, but he shot down the education-tax credit that’s being pushed by Cardinal Timothy Dolan.

Silver outlined his end-of-session priorities on Wednesday, telling reporters that he would be open to taking up anti-heroin legislation that has passed the state Senate as well as a push to increase the number of family court judges in the state.

“I think heroin is becoming a big problem in this state and we have to address that,” Silver said. “I would like to come to an agreement on new family court judges. That’s something we desperately we need and we have the money in the budget to do it.”

And the speaker made another push for the Dream Act, legislation that provides tuition assistance to undocumented immigrants, but failed in the state Senate earlier this year.

“I would like to still see a Dream Act pass in this state,” Silver said. “I think it’s something we owe to young people, which is opportunity.”

The Dream Act legislation has often been discussed as being linked to an education tax credit, which is aimed at private and parochial school donations.

But Silver on Wednesday rejected the tax credit, saying it “doesn’t make any sense” given the combined rebate can be as high as $1.35 for a $1 contribution.

Dolan has appeared in a TV ad pushing both state lawmakers and Gov. Andrew Cuomo to take up the education-tax credit legislation.

Updated: The concerns Silver raises are addressed by a measure backed by Assemblyman Michael Cusick.

“Nobody wants that to happen and it’s already been addressed by Assemblyman Cusick in his legislation,” said Bob Bellafiore of Stanhope Partners.