The Sewel Convention, which is enshrined in the devolution legislation, states Westminster "would not normally legislate with regard to devolved matters in Scotland without the consent of the Scottish Parliament".
But Scottish Labour's Brexit spokesman Neil Findlay said: "As the party that delivered devolution, Labour will always seek to defend and strengthen it.
I hope the UK Government will make this simple change before the legislation is passed and respect the devolution settlement Scotland voted for".
Theresa May has the power to force the Bill through without getting the consent of Scotland.
Plaid AM Adam Price said: "We are joining a very select club of national Parliaments, if we pass this motion today, that have voluntarily made a decision to cede their own authority".
Lawmakers in the devolved Edinburgh assembly voted by 93 to 30 to refuse "legislative consent" for the highly-contested European Union (Withdrawal) Bill now being debated by the British parliament.
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The UK Government has balked at this on around 24 of the powers being repatriated from Brussels, unwilling to give MSPs an effective veto.
SNP member of the Scottish parliament (MSP) Christina McKelvie said on Tuesday that clause 11 would allow Ms May's government to start dismantling the devolution framework on which the Scottish parliament is based.
"The solution, as this Parliament has agreed, is straightforward".
As the EU Withdrawal Bill covers areas which are devolved to both Scotland and Wales, the parliaments in Edinburgh and Cardiff are required to vote on this. On that occasion the UK Government responded by removing those parts of the Bill. He said the government would press ahead with the Bill but suggested it would be open to amending it to reflect Scottish concerns.
In an article in the Sunday Herald newspaper following the Scottish government's rejection of the deal, Scottish First Minister Nicola Sturgeon said: "If our principled stance means the SNP are the only or the last party standing, defending the founding principles of devolution, then so be it". "It is deeply regrettable that the SNP has refused to take it".
MSPs voted against the legislation by 93 votes to 30, with the Scottish Nationalists backed by Liberal Democrats and Labour.
He added: "It's obvious that the Greens will, as always, back the SNP today".
"The Scottish Parliament has spoken loudly and clearly - it's now up to the United Kingdom government to respect that vote and ditch their power-grab", SNP Scottish lawmaker Ash Denham said in a statement.