CHARLOTTE, N.C. ( TheStreet) -- Not everybody was pleased by last week's show of unity between US Airways ( LCC) CEO Doug Parker and the leaders of the three largest unions at American Airlines ( AMR). The American labor leaders appeared with Parker when he spoke last week at the National Press Club in Washington. Parker praised the three as leaders who "have acted in the best interest of their members and American Airlines." Asked where US Airways union leaders were, he responded: "Hard at work, working to represent (US Airways employees)." But the International Association of Machinists, the largest union at US Airways with about 6,000 active fleet service workers and 3,500 active mechanics and related workers, said Parker should spend time negotiating open contracts with the workers at US Airways before he gets too close to leaders of American unions. "We ask that instead of hobnobbing with other airlines' unions, Parker get serious about reaching an agreement with his own employees at his own airline," said Rich Delaney, IAM District 141 president, in a prepared statement. "Parker swiftly negotiated agreements with American's unions yet continues to ignore his own employees." Added Tom Higginbotham, IAM District 142 president, in a prepared statement: "Doug Parker does not have the support of the Machinists Union. Any possible support from his own employees must be earned. Concluding contracts negotiations and guaranteeing our seniority would be a good start." In April, US Airways announced that it has signed tentative deals with the three largest American unions. But US Airways pilots and flight attendants still work under deals negotiated before or during a bankruptcy that concluded in 2005, while contracts with the IAM workers are currently open. Early this month, the leaders of all of the US Airways unions gathered at the headquarters of the U.S. Airline Pilots Association in Charlotte. They agreed to form a United Labor Committee to protect workers' interests during the merger effort. The status of the US Airways unions could be threatened by a merger because the work groups at American are all larger and are represented by different unions. Mechanics and fleet service workers are represented by IAM at US Airways and Transport Workers Union at American. Agents are represented by Communications Workers of America at US Airways and unrepresented at American. Flight attendants are represented by Association of Flight Attendants at US Airways and Association of Professional Flight Attendants at American.