HARTFORD, Conn. — 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 (THEHM’-his KLEHR’-ih-dehs) and Democratic House Speaker Joe Aresimowicz (ehr-eh-SIM’-oh-wits) 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.