Umenyiora, 29, worked with the first-team defense Monday, splitting snaps at right end with second-year pro Jason Pierre-Paul.
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"I hope it's all behind me, that's all. I'm going on," Coughlin said after the two-hour workout at the Timex Performance Center. "He's here. He wants to work. He wants to be a part of the team. We certainly want him to be. We want it all. We don't want a part of it, we want it all. I'm hoping that's the way it is."
While Umenyiora practiced for the first time since reporting to camp 17 days ago, he isn't happy.
Umenyiora maintains Giants general manager Jerry Reese promised to rework the final two years of his contract and failed to do it. Reese offered the nine-year veteran a contract laden with incentives this year, but Umenyiora told The Associated Press in an email Sunday that was unacceptable.
Umenyiora, who tied for the team high with 11.5 sacks and led the NFL with 10 forced fumbles last season, will play this season under the terms of his current contract. It will pay him $7.1 million over the next two years.
Fellow defensive end Justin Tuck said Umenyiora was in good spirits Monday, but he noted that didn't mean his buddy was happy.
"Just because he is back on the football field doesn't mean this saga is over," Tuck said. "Again, he is doing what he thinks is best for this football team and himself."
Tuck believes that Umenyiora will continue to work with the Giants to resolve his contract dispute, adding he doesn't think it will either affect how the defensive end plays or how the team prepares for games.
Umenyiora, who has been bothered by a sore knee for the past 10 days, showed quickness during individual drills early in practice and held his own in 11-on-11 drills.
"He jumped right in there and tries to beat the ball like he normally does," Coughlin said. "It was good to see."
Pierre-Paul, who had two sacks during Saturday night's preseason loss to the Carolina Panthers, wasn't upset sharing the right end job with Umenyiora.
"It makes the offense have a little hesitation, and when we have all three of us out there in the Osi package, they don't know what to do," Pierre-Paul said. "So, it is good. Osi is back."
Teammates also said Umenyiora's situation was never a major problem. Quarterback Eli Manning said he was so focused on the offense that he believed Umenyiora's absence was only a minor distraction.
"I haven't been answering questions on it," Manning said. "It hasn't been a main concern. Right now, it's something that had to get worked out, but we had other things we had to worry about."
Cornerback Terrell Thomas said having Umenyiora back in the lineup will put pressure on opposing quarterbacks and make his life easier.
"He's been in meetings, been alert and not made a fuss about it," Thomas said. "He's been talking to the younger guys at practice and doing what he has to do. Hopefully, he comes back healthy and makes us stronger as a team."
"He is a tremendous football player and a great teammate, so having him out here is going to be awesome for us," Canty said. "We are just putting more bullets in the gun."
Copyright 2011 by The Associated Press