Holyrood's constitution committee says it still wants a deal secured between Westminster and Edinburgh in the row over powers coming back from Brussels after Brexit.
But failing this, it concludes in a report today: "The Committee recommends that the Parliament does not consent to Clause 11 and Schedule 3 of the Bill."
MSPs will vote on the legislative consent motion (LCM) at Holyrood next week.
Scottish Secretary David Mundell has said the UK Government has already indicated it will not shift on this issue.
The call to withhold consent had the backing of Labour and Green members of the committee.
Although the UK Government can press ahead with the Brexit Bill in Scotland if MSPs reject it, this would mark an unprecedented constitutional crisis in the two decades of devolution.
Constitution committee convenor Bruce Crawford said: “There is scope for a reasonable solution to be found. If there is parity and both governments are treated equally, and both are bound by political agreement, then this can be amicably resolved.
“The Secretary of State for Scotland said he trusted the Scottish Government, and I welcome that, but it is time for his trust to be put into practice.
“And for that reason, our Committee has reached the conclusion that Clause 11 and Schedule 3 of the EU (Withdrawal) Bill should be removed and for reciprocal political commitments to be included in the Inter-Governmental Agreement.”
But Mr Crawford added: “The Committee remains deeply concerned about the lack of any statutory provision within the Bill for UK Ministers to seek the consent of Scottish Ministers or the Scottish Parliament to legislate in devolved areas, especially given that the Sewel Convention does not apply to subordinate legislation."