Separately, the pilots' union board was meeting Tuesday to reconsider whether to let members vote on American's final contract offer.
Tuesday's developments raised the prospect that American could negotiate voluntary cost-cutting deals with all three of its labor unions, which seemed unlikely just a week ago.
The Transport Workers Union said that negotiators for American's mechanics expected to meet soon with company officials. Last month, mechanics rejected a company offer that was approved by five smaller groups of ground workers.
The Association of Professional Flight Attendants said Monday night that it was seeking to resume negotiations too. Company spokesman Bruce Hicks said American looked forward to more talks with the flight attendants.
The unions are facing a Friday deadline for U.S. Bankruptcy Judge Sean Lane to rule on whether American can throw out labor contracts and temporarily impose its own terms for pay, benefits and working conditions.
The judge has already postponed a decision twice, including a one-week delay until Friday to give the Allied Pilots Association more time to consider American's latest offer. The union said its board needed more clarification from American on some terms.
American had sweetened its offer to pilots, proposing a 17 percent cut in pilot costs with no layoffs instead of an earlier 20 percent cut that included eliminating 400 pilot jobs.
The unions all back a potential takeover of American parent AMR Corp. by US Airways Group Inc., which has offered fewer layoffs and other cuts than American proposed. AMR filed for bankruptcy protection in November.