Assembly Speaker Sheldon Silver on Monday defended the agreement in the $138 billion state budget that creates a public financing system only for the state comptroller’s race, but added he hopes a broader public-matching program will eventually be approved.

“Hopefully we’ll early on get either the complete thing done for the next campaign cycle or at least a more realistic experiment for the next campaign cycle,” Silver told reporters.

Silver noted that DiNapoli, a Democrat and supporter of public financing, had initially proposed a public financing program for his campaign as a sort of pilot program.

But the budget’s program would make the public financing system take effect this election cycle as DiNapoli gears up to run for another four-year term.

DiNapoli plans to not opt in to the program.

DiNapoli, of course, is a product of the state Assembly, having represented a Long Island district before his colleagues elected him to fill the unexpired term of Alan Hevesi, who resigned in 2005 before officially taking office for a second term.

The inclusion of the public financing program for the comptroller’s race has also inflamed good-government groups as well as advocates for the program who wanted a statewide system.

Silver with reporters noted Senate Republicans had initially opposed any form of public financing. The Democratic-led Assembly has approved a statewide public financing system multiple times.

“That’s a crack in that armor in that they agreed to this and hopefully as we go down the road, they’ll agree to the complete system,” he said.

The program has again stoked talk in political circles of the cold relationship between Cuomo and DiNapoli.

But given the comptroller’s roots in the Assembly, the move was also surprising. Silver said he understood why DiNapoli is choosing not to participate in the program.

“This is not much of a change to it, but I can understand that it came late in the process,” he said. “The re-election campaigns were already underway and that’s always been an option we’ve given in any kind of public financing system. He’s electing that option, he’s still my friend, I still intend to vote for him.”