Some 59 parliament members on Tuesday asked the speaker to demand the government withdraw the proposed legislation and give more time for further discussion.
The main objection was that unions were not consulted and that the cabinet seemed bent on "stifling its (trade unions') national and developmental role".
Last week, the cabinet approved the draft law with the aim of regulating unions and barring them from engaging in politics.
The proposed legislation calls for establishing a one-man one-vote principle rather than elections based on lists, and stipulates that voters choose a committee which in turn will elect union representatives and a board.
On Sunday, the president of the Jordanian Bar Association resigned after accusing the government of banning professional unions in the kingdom.
Husain Mijali said his decision was also a protest against a proposed new law for union elections.
The voting mechanism in the new law, to be presented to parliament on Wednesday, will prevent any block from gaining a majority in the Association Council, he said.
This "violates the constitution and law" and is "tantamount to banning professional unions in the kingdom", he added.
Jordan has regularly been censured for interfering in trade union affairs.
In a recent statement, the International Confederation of Free Trade Unions condemned Jordan for attempting to prevent freedom of association and for meddling in union elections.
However, the Jordanian government has previously said that unions were violating the law by engaging in politics.