HARTFORD, Conn. — With no deal on a new, two-year state budget in sight, Gov. Dannel P. Malloy on Monday made a renewed pitch for legislators to pass his temporary “mini budget” in the meantime and help protect services to the state’s neediest residents.

The Democrat appeared in Hartford at HARC Inc., a nonprofit organization that serves people with intellectual disabilities. Like other nonprofit social service agencies across the state, HARC is facing funding cuts because Malloy is running the government using his limited spending authority and executive powers.

Malloy told a group of HARC officials and family members of HARC clients that he wishes he didn’t have to make cuts that affect initiatives such as employment programs and adult day services. But he said he has no choice because the General Assembly didn’t pass a two-year budget or his temporary budget before the fiscal year ended June 30.

“I’m not happy. I’m trying to have you understand that,” he said of the cuts. “If we’re not going to have a permanent budget … in a matter of days, then let’s get beyond that and let’s do something that at least brings about a level of relief. That’s what I’m looking for.”

House Democrats had hoped to vote Tuesday on a new two-year budget but instead plan to hold a closed-door meeting to discuss the status of budget negotiations. House Speaker Joe Aresimowicz, D-Berlin, who previously opposed the idea of passing a stop-gap budget for at least 90 days, said Monday that he still doesn’t think it’s a good idea.

“Every day that we delay and do not sit down and negotiate in earnest toward a full two-year budget is a step back, and that is the only thing a so-called ‘mini budget’ would do,” he said in a written statement, adding that lawmakers need to “solely focus” on moving Connecticut forward and providing stability to nonprofit agencies, municipalities and businesses.

Aresimowicz said last week that he was optimistic a new, two-year budget that covers a projected $5 billion deficit will be passed by July 31. A new, two-year budget is roughly $40 billion.

Asked if he thought a vote by July 31 is possible, Malloy noted that the state’s budget is complicated. For example, lawmakers still don’t know if the state employee unions will agree to $1.5 billion in concessions over two years. Votes were wrapping up Monday night. Tallies were expected to be revealed Tuesday.

HARC officials and family members said they want a state budget as soon as possible. They’re particularly worried about six looming furlough days, when no employment or day support activity will be reimbursed by the state. The first one is July 26.

Janice Marden, vice president of employment and day services at HARC, said there are 107 Hartford-area clients employed at places like hospitals, insurance companies and food service companies. She said those entities rely on HARC workers daily and couldn’t accommodate furloughs, potentially putting the employment collaborations at risk.

“We do some very vital work. For us not to be there would be a loss to the companies,” she said. “This is going to have devastating effects to our employment opportunities.”

In the meantime, she said, HARC is considering absorbing the cost, which she estimated to be about $25,000 to $30,000 per furlough day, to protect the jobs for the HARC clients, some of whom have worked at the same site for decades.