Further job cuts are on the way before June 1 at General Motors Corp., Chief Executive Fritz Henderson said this morning in a conference call with reporters.

“There will be futher reductions in manpower … but we don’t have those finalized today,” said Henderson, who became GM’s leader nearly three weeks ago after Rick Wagoner stepped down from the post.

No major developments were announced during Henderson’s update of the automaker’s restructuring plan. Last month, the Obama administration said plans submitted to the goverment by GM and Chrysler were not adequate and deeper cuts had to be made. Chrysler has until the end of this month to cut costs, get labor concessions approved and finalize a deal with Fiat. GM has until the end of May for its own slimdown plan.

Locally, GM employs more than 1,800 workers at its assembly plant in Wentzville, where full-size vans are made.

Here are some other points that Henderson addressed:

Concessions with bondholders: “We’ve had discussions with them, but I’m not going to go into what may or may not be on the table at this point.” Talks between GM and the United Auto Workers are continuing, he added.

Bankruptcy possibilities: Henderson said he still thinks bankruptcy is probable, but he reiterated that GM’s preference is to restructure outside of court. “It’s still feasible to do that, given the time frame, but the clock is ticking.”

GMC and Pontiac brands: Henderson dismissed reports that GM could shed GMC and Pontiac. In its February report to the U.S. Treasury, GM said it planned to focus on four core brands — Chevrolet, Cadillac, Buick and GMC. Pontiac would be a niche brand, and the automaker would review or sell Hummer, Saab and Saturn. Near the end of the conference call, he said: “I talked about a four-core brand strategy, not a two-core brand strategy.” He did acknowledge, though, that all brands are being reviewed. “We’re looking at the purpose and reasons for being for all our brands.”

Hummer: GM will make a final decision by the end of this month on the brand, Henderson said. It has bids from three potential buyers.

Whether a GM-Chrysler partnership is still an option: “You could move the chess pieces around a lot,” Henderson said. “We looked at Chrysler last year and set it aside. I couldn’t even imagine working on something like that in the current environment.” GM is focused on improving its own operations right now, he added.