U.S. and Japanese textile unions said they hoped an "orderly system" of world textile trade will be maintained after the agreement that governs the trade expires under a current proposal.

But U.S. union leaders say the outlook for such order is poor."We are not very hopeful that we will come out very well in this process," said Jay Mazur, president of the International Ladies' Garment Workers' Union.

"We've always felt that the (U.S.) government doesn't have the best interests of the apparel industry at heart."

Under a plan to complete the Uruguay Round of world trade talks, parties to the General Agreement on Tariffs and Trade are proposing to phase out the Multi-Fibre Arrangement.

The MFA is an international umbrella agreement that limits world textile and apparel trade. It has been criticized by major exporting countries as overly protectionist.

U.S. textile manufacturers have lobbied hard against the planned phase- out, claiming expanded quotas will result in a tidal wave of low-cost Asian imports that will sink the U.S. industry.

Mr. Mazur and Jack Sheinkman, president of the Amalgamated Clothing and Textile Workers Union, spoke to reporters here this week at the end of a two- day conference with officials of Zensen, a federation of Japanese unions.

A joint statement issued after the conference called for the maintenance of orderly trade in textiles after a 17-month extension of the MFA negotiated last year expires at the end of 1992.

Improved trade restrictions to be imposed under GATT are supposed to take the place of the MFA once it expires. But, Mr. Sheinkman pointed out, the Uruguay Round may not be resolved in time to replace the MFA.

"We are not at all sure there will be a resolution to the Round," Mr. Sheinkman said. "You cannot eliminate the MFA and not substitute with something" that will meet the needs of both the United States and other countries, Mr. Mazur said.

U.S. officials say, however, that if the Uruguay Round is not completed by the end of the year, they will negotiate to extend the current terms of the MFA. But textile-exporting countries are likely to oppose a roll-over unless quotas are liberalized to their benefit, a U.S. official said.