FRANKFORT, Ky. — Kentucky’s races for governor and other statewide offices would take place in presidential election years, under a proposed constitutional amendment that cleared the state Senate on Thursday.

The lead Republican supporter of the proposed ballot measure said Thursday the change would boost voter turnout and save money for the state and counties by reducing the number of elections. A top Democrat, however, saw a different motive — to further boost GOP chances of winning statewide offices by linking those elections to the presidential race.

The proposal was passed on a 24-11 vote in the Republican-led Senate and now goes to the House, where a similar measure has been introduced in the GOP-run chamber. If one of the measures clears both chambers, it would go on the November ballot.

The measure would change when the governor, lieutenant governor, attorney general, secretary of state, treasurer, auditor and agriculture commissioner are chosen, starting in 2024 and every four years after that. Now, those statewide officials are chosen in odd-numbered years.

If the proposed constitutional change is ratified by voters statewide, those offices would still be up for election in 2019. But the winners of those elections would serve five-year terms. After that, those statewide elections would coincide with presidential election years.

The Senate proposal’s lead sponsor, Republican Sen. Chris McDaniel of Taylor Mill, said the change would save money, simplify elections and improve turnout.

“I can’t imagine anything more democratic, more bipartisan than wanting to save money, make elections easier and improve voter participation,” he said.

Senate Minority Floor Leader Ray Jones, D-Pikeville, said the change was driven by politics.

“It’s not about saving the state money,” Jones said. “What this is really about is putting Kentucky into the presidential election cycle in hopes of the GOP gaining an advantage.”

Kentucky has moved solidly toward Republicans in recent presidential elections.

Jones and Sen. Reggie Thomas, D-Lexington, said state issues could be overshadowed by federal matters if races for statewide offices coincide with presidential elections. “The last thing we need is a nationalization of political races that affect state issues,” Jones said.

Sen. Wil Schroder, R-Wilder, downplayed those concerns. He noted that federal and state issues already are mixed into the same elections in Kentucky when state legislative candidates run on the same ballot as congressional candidates.

“Our voters are sophisticated enough to research the candidates, research the issues and realize what pertains to the federal level and what pertains to the state level and sort that out for themselves,” he said.

It was the second straight day the Senate passed a proposed constitutional amendment.

On Wednesday, senators backed a proposal to award constitutional protections to crime victims, which would give them a greater voice at their alleged assailants’ criminal proceedings. That measure now goes to the House.

Lawmakers are considering a stack of proposed constitutional amendments this session.

Ballot measures seeking to change Kentucky’s Constitution have appeared infrequently in recent elections. The last time a constitutional amendment appeared on the statewide ballot was in 2012, and since 2002 four proposals have been on the ballot, according to the secretary of state’s office.