Both Democratic and Republican legislative leaders say they have concerns with Gov. Dannel P. Malloy’s plan to close the $389 million deficit in Connecticut’s current budget.

The Democrat’s proposal includes $33 million in immediate cuts that affect everything from financial help for elderly renters to funding for regional vocational-technical high schools. Some of Malloy’s ideas require legislative approval, such as not paying cities and towns more than $19 million in June from the state’s share of slot machine revenues at the two tribal casinos.

House Republican Leader Themis Klarides and Democratic House Speaker Joe Aresimowicz say the governor’s proposed cuts for the fiscal year ending June 30 should be part of the talks for the new two-year budget that begins July 1.

Those negotiations begin next week.