The drive by state employee union leaders to win ratification of a tentative concessions agreement ended the week with a flurry of votes in favor of the deal by major clerical, higher-education and health-care bargaining units.

By Friday night, three of the 15 unions in the State Employees Bargain Agent Coalition had ratified the deal negotiated a month ago with the administration of Gov. Dannel P. Malloy. Among them the three represent almost 10,000 of some 45,000 union members, according to SEBAC.

No union has rejected it.

“We remain cautiously optimistic,” said Larry Dorman, a spokesman for the coalition.

To ratify the tentative agreement, 14 of the 15 unions must vote yes.

Sources initially said Friday that a fourth union also had ratified.

The complex voting is slowly unfolding, inching toward a deadline of June 24 to complete the balloting. The 15 unions are composed of 34 bargaining units, and some bargaining units are further divided into several union locals.

Eleven of the 15 unions consist of a single bargaining unit. The largest, AFSCME Council 4, has nine units, CSEA/SEIU Local 2001 has seven, AFT Connecticut has five, and District 1199/SEIU has two.

Most union members can cast two votes: One is on the SEBAC agreement, which covers health and retirement benefits for all members; the other is on wage and job-security issues, which are negotiated by individual bargaining units.

That means that if the SEBAC agreement is approved, all union members will be subject to the health and retirement provisions, whether their individual bargaining units backed it or not. But employees in units that vote down the deal will not benefit from the four-year no-layoff guarantee included in the agreement. They won’t be subject to the agreement’s two-year wage freeze, but they also won’t be assured the 3-percent raises it provides in each of the following three years.

SEBAC is not revealing results of the voting, but some individual bargaining units have announced the votes. Sources have confirmed others.

On Friday, votes were tabulated for two unions in favor of ratification: District 1199/SEIU, which represents health care workers; and AAUP at UConn, representing faculty.

The smallest of the 15 unions, the Connecticut Federation of School Administrators, previously had approved ratification. The union represents principals and assistant principals at 18 state technical and vocational high schools.

Vote results from some individual bargaining units also have been disclosed, although their significance is less clear without knowing the results for the entire union. A dozen bargaining units now have voted in favor of ratification, including University Health Professional at UConn and UConn Professional Employees, two AFT units representing about 4,100 members.

Four of the nine units comprising AFSCME Council 4 also have voted for the agreement, including those representing clerical, higher education, technical college and Charter Oak College workers. In all, they represent about 5,300 employees, according to SEBAC.

Two other AFSCME units representing 1,600 judicial and criminal justice employees have voted no, as have two of three locals in the 4,800-member Correction unit. The third is scheduled to vote next week.

Another large AFSCME unit, which represents thousands of employees in human and social service jobs, also will vote next week, as will a smaller unit representing state university administrators.

When all the AFSCME units have voted, a total vote of the entire union will be compiled on the SEBAC agreement. It was unclear Friday how the other unions with multiple bargaining units will reach a unified position if the units split.

“It is an internal question for each of those unions,” said Daniel Livingston, the chief negotiator for SEBAC.

The governor said Friday afternoon, before some of the positive results were known, that he was neither encouraged, nor discouraged by the voting results.

“I don’t run these elections,” Malloy said. “I’ve done everything in our power to avoid having to lay people off. But it’s been very clear since Feb. 16 that we needed the cooperation of our employee base. We certainly have that among the leadership. The membership has to make a decision. My path is fairly clear, one way or another.”

This story originally reported a fourth union had ratified, based on union sources.