The administration of Gov. Dannel P. Malloy announced a new tentative concession agreement at 10:04 p.m. Friday, setting the stage for another attempt by a coalition of state employee unions to ratify a deal that could stave off mass layoffs and deep budget cuts.

“I am pleased that an agreement has been reached,” Malloy said in a statement. “So that there is no confusion, let’s be clear about what this clarified agreement is. This agreement saves the same amount of money as the last agreement- $1.6 billion over 2 years, $21.5 billion over 20 years – and it contains all of the same cost-saving provisions as the last agreement.”

SEBAC followed by minutes with a statement that the new tentative deal addresses a major concern of union members: that a new wellness program was not the first step toward placing state employees in a new health plan modeled after SustiNet, the state’s failed attempt at establishing a universal health system.

“The agreement clarifies unequivocally that the now-dead SustiNet health reform legislation has nothing to do with the plan — and never will,” the union statement said.

All layoff notices issued to unionized workers in recent weeks will be rescinded, the union said.

Accompanying the union statement was a package of information, the first step at trying to frame the new deal in a better light than the previous tentative agreement, which was approved by 11 of the 15 member unions, too few under bylaws requiring support by 14 of 15. The SEBAC bylaws were changed Monday to allow ratification by a simple majority of eight unions.

No details were immediately available on plans by individual unions to hold ratification votes. An outcry followed a suggestion earlier this week by a union spokesman that it was possible some unions that approved the first tentative agreement might not need a second vote if a new deal was essentially unchanged.

Concession talks had ended for the night Friday without an immediate announcement or comment by the administration  or the coalition of state-employee unions, but labor showed signs it was thinking about how to urge passage of a new deal.

At 7 p.m., the State Employees Bargaining Agent Coalition posted a notice announcing it was taking strict control over its Facebook page, an indication the unions already were trying to take control of messaging once a new tentative agreement is announced.

“Beginning today we will recapture the original intent of the Facebook page and make it a source of information for union leaders’ discussions and details of any agreement that may be reached,” said the posting by Matt O’Connor, a spokesman for SEBAC.

After a 24-hour freeze on comments to the press, the posting was the first tangible sign that the the unions were looking ahead to the next, crucial phase of the second attempt to strike a deal for labor savings, ground Malloy staked out in proposing his budget Feb. 16.

The second round of concession talks was difficult as labor sought changes to mollify its members, while Malloy faced a political disaster if he had yielded ground from the initial deal, which Republicans had denounced as far too generous to labor.

On Friday night, Malloy stressed how little had changed.

“So what’s changed?” Malloy said. “The health care language has been clarified to make it crystal clear that state employees are not being put into a new healthcare system called ‘SustiNet.’ There is language in the agreement that will allow the state to recoup the money state employees will be getting from a raise that just went into effect. And the effective date by which state employees can retire before any of these changes go into effect has been changed from September 2, 2011 to October 2, 2011.

“That’s it. No other changes from the first agreement. I said all along that I was only willing to clarify terms from the last agreement, and that’s what we’ve done.”

Malloy had vented earlier in the day as the effort to secure a second union vote on a concessions package threatened to drag into the weekend, but he seemed more upbeat at 6 p.m. as he awaited word of a deal from his negotiator, Mark Ojakian.

The governor, who one week ago announced 6,500 job cuts and more than 20 facility closures to achieve the $1.6 billion savings tied to the concession package rejected last month, reaffirmed his pledge not to substantively revise the initial deal.

“I remain hopeful, but quite frankly it’s taken longer than it should,” Malloy told reporters during a public event earlier in the day at the Manchester Senior Center. “I don’t think there is much to talk about.”

The governor has said repeatedly that he is willing to clarify details of the concession plan, which included a two-year wage freeze, a health insurance premium hike and a higher deductible for employees who don’t participate in a wellness program, as well as new restrictions on pensions and other retirement benefits.

That wellness program has been a source of confusion and controversy.  Another challenge involves canceling raises of about 2.5 percent that many unionized employees received on July 1. And the governor said certain details need to be explained in clearer terms to rank-and-file workers.

“This agreement got shot down once. It could get shot down again,” he said. “It will get shot down again if people don’t do their jobs and explain to people why this is necessary.”

But while clarification is necessary, Malloy added, the basic details must remain in place.

“I agree to the agreement we agreed to,” the governor said, adding he wouldn’t be surprised if some in labor hope to change the deal. “Delay for delay’s sake doesn’t make any sense. We’re not going to renegotiate.”

The governor said either the concession deal, or his alternative plan to impose on the largest budget cuts in recent state history, has to occur because Connecticut can’t afford its current workforce.

“I think people have a decision to make whether they want a Connecticut that moves forward and addresses its problems through a negotiated process or whether we don’t get to that point and other steps have to be taken,” he said.

State Employees Bargaining Agent Coalition spokesman Matt O’Connor could not be reached for comment late Friday afternoon. O’Connor has said the coalition is committed to reaching a deal with Malloy, adding that the alternative job and programmatic cuts would be “catastrophic” to employees and to the services they provide.

The coalition revised its bylaws Monday to allow contract changes to be ratified provided eight of the 15 unions vote in favor, and provided they represent a bare majority of total SEBAC membership. The original threshold was 14 out of 15 unions and 80 percent of membership.

The deal that was rejected last month had won support from 11 unions, with 57 percent of participating members voting in favor.

The governor had added that he likely isn’t the only one waiting to hear if labor will grant concessions. More than 1,850 employees had received layoff notices through Wednesday.

“I think people want to hear,” Malloy said. “And it ain’t going to get any better.”

Most of those 1,851 workers still are on the job in accordance with the warning period spelled out under their respective union contracts. Most unionized workers receive between two and eight weeks layoff notice before they must leave their jobs.

Though an approved concession deal would reverse nearly all layoffs to date, and others ordered between now and potential ratification, it would not cancel all of them. The original package allows the administration to eliminate positions in connection with planned consolidations.

Malloy and the General Assembly agreed to a net reduction of 23 departments and agencies in the new state budget, from 81 to 58. Technically, they removed 28 entities via consolidation, but they also created five new ones, eliminating a net total of 68 positions in the process.