NEW YORK (CNNMoney.com) - GM Chairman and CEO Rick Wagoner tried to assure shareholders that the company is on track to ending its troubles, although he conceded that there are a number of tough problems still facing the automaker and passed up a chance to say its worst troubles are behind it.

Speaking Tuesday at GM's annual shareholder meeting in Wilmington, Del., Wagoner warned that one cost cutting target - an effort to trim supplier costs by $1 billion - would likely fall short. And when questioned by reporters, he held out the possibility of more plant closings beyond the 12 already planned through 2008.

GM Chairman and CEO Rick Wagoner.

While he said he expects year-over-year improvement from the quarterly losses of 2005, he believes U.S. auto sales are likely to see further market-share losses.

Shareholders, who have seen a drop in their share price, a 50 percent cut of their GM dividend and billions in continuing losses on the company's core automotive operations since last year's shareholder meeting, responded by giving majority support to two resolutions calling for changes in the way that its directors are elected. The votes were described by one activist as a strong rebuke to the leadership of the embattled automaker.

But the shareholders did not support other resolutions, including one that called for splitting the jobs of chairman and CEO, one which would have ended stock options and another calling for the return of performance bonuses paid to executives if the company restates financial results. The board can ignore all the votes, if it so chooses.

Shares of GM (Research) lost about 3 percent in late trading following Wagoner's remarks.

The GM shareholders have seen the stock perform well this year, rising 31 percent year to date, making it the best performing component of the Dow Jones industrial average. But shares are down nearly 16 percent from where they were at the 2005 annual meeting, and they've also lost about 12 percent in just over the last week.

Wagoner said that the company has made good progress on its turn around plans, and he's confident it will be able to cut $7 billion in costs out of its North American auto operations. But he said higher raw material costs "will make it very difficult to achieve" the $1 billion cost savings target for GM's supplier purchases.

"It's important to understand that our goal in this restructuring is not just to change GM's bottom line from red to black. Our goal is to structure GM for sustained profitability and growth," he said.

"In the past year, we've made some big moves, and we've made a lot of progress," he added. "Looking forward, we are optimistic about prospects for GM and the auto industry. But no misconceptions, here - we know that there is plenty of hard work in front of us."

Under tasks still facing GM, Wagoner mentioned finalizing the staff cuts that come from various retirement and separation bonuses that GM is offering its hourly workers, participating in a labor agreement between the UAW and its former parts unit Delphi, and the introduction of new models.

Wagoner did not give any details during his prepared remarks or during his press conference on how many workers are likely to take GM offers of up to $140,000 to leave the company as part of its cost-cutting plans. Several analysts have upgraded the stock recently in anticipation that more workers than originally expected would take the offers, which would allow GM to cut labor costs faster than earlier estimates.

In response to reporters' questions, he said he is optimistic about talks at Delphi, although he conceded, "There are days you feel great, that you feel like it can accomplished quickly. There are days that are it seems pretty tough....In any given set of negotiations, you have these ebb and flows. But the direction is positive."

In response to a reporters' question about the GM plant in Wilmington, Wagoner wouldn't give assurances that GM will be able to stop with its current plant closing plans, saying that would depend upon the company's efforts to improve its financial position.

When another reporter asked him if he could now say that the worst was over for GM, he also would not give any such assurance, although he said, "Certainly the first quarter is saying we're making rapid strides in the right direction."

In response to reporters' questions, Wagoner vowed GM, the nation's No. 1 automaker, would stick with its policy of trying to limit the use of costly sales incentive programs to boost U.S. sales, even if it means that the automaker continues to lose U.S. market share. But he also warned that the company is likely to see further declines in U.S. sales in June and July, compared to a year ago when GM used its' popular "employee pricing" program to draw buyers to showrooms.

One of the successful shareholder resolutions calls for directors to get a majority of votes among shareholders in order to be elected. Directors now not facing an opposing slate of candidates can be elected with only a miniscule number of votes cast in their favor, since shareholders are only given the chance to vote for a candidate or withhold their support for that candidate. GM said that resolution got about 54 percent support.

The other successful resolution would allow shareholders to give multiple votes to one or more board candidates by withholding votes for other candidates. GM said that resolution got about 58 percent support. That proposal, which would help the chances of competing candidates to the board to be elected, is known as cumulative voting.

"This is huge," she Nell Minow, editor of The Corporate Library, a shareholders' rights watchdog, about the votes. "Of course the GM board is within its rights to pretend this vote never took place, but that would be very poor judgment on their part. I believe they need to look at this vote as a vote of no confidence in directors and management and they should be responsive."

Minow said that only 37 Fortune 500 companies have cumulative voting procedures, while about 80 of those companies have instituted majority voting within the last year.

Wagoner said that the two resolutions would be referred to the board for consideration, and that given the support the resolutions had received in past years, he was not particularly surprised by the result. The GM board had opposed both measures.

Asked by reporters how he felt more secure in his job with the defeat of the resolution seeking to split his two jobs, Wagoner said, "I'm not worried about security. I'm just trying to do the right thing to keep the business on the right track."

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