Andrea Leadsom, Leader of the House of Commons, said on Tuesday that this had been a "full and frank exposition", and that releasing the full advice would set a unsafe precedent.
In a historic first, the British Parliament found the government of Prime Minister Theresa May in contempt on Tuesday for failing to release in full the advice it received from the country's top law officer about the terms of exiting the EU.
In dramatic scenes at Westminster, the Government bowed to pressure to publish the "final and full" legal advice to Cabinet on the deal after MPs voted by 311 to 293 that its failure to do so amounted to contempt.
Before the debate, May's government faces another showdown with lawmakers over legal advice about the Brexit deal.
"The British people want us to get on with a deal that honours the referendum and allows us to come together again as a country, whichever way we voted", she will tell lawmakers on Tuesday, according to excerpts of her speech.
The matter will be debated by the Commons, and could lead to a vote to suspend the Attorney General for five days.
Shadow Brexit Secretary Sir Keir Starmer said Tuesday's vote had "huge constitutional and political significance". "By treating Parliament with contempt, the Government has proved it has lost its majority and the respect of the House".
The prime minister needs roughly 320 votes in the House of Commons to secure the approval of her deal.
Pro-EU lawmakers said they had made the prospect of a "no-deal" Brexit less likely by securing an amendment giving Parliament more power to guide the government's next steps if the deal is rejected on December 11.
With the fragility of the government's parliamentary majority laid bare, May opened a five-day debate on her plan for how the United Kingdom leaves the European Union, well-aware an even more significant defeat is on the horizon.
Minutes earlier, the Government's attempt to have the contempt motion kicked into the long grass by referring it to the Committee of Privileges had been defeated by 311 votes to 307, majority four.
Mr Bercow was responding to a call from senior MPs in six parties - Labour, the Lib Dems, the SNP, the Democratic Unionist Party, Plaid Cymru and the Green Party - for contempt proceedings to be launched.
Commons Leader Andrea Leadsom said: 'We've tested the opinion of the House twice on this very serious subject. Rejecting it would leave the United Kingdom facing the prospect of a chaotic "no-deal" Brexit, but May's chances of winning majority backing for the deal appear slim.
Majority opposition, however, would force her government to put forward a new plan within 21 days.
In an opinion prepared for the European Court of Justice (ECJ) in Strasbourg, the advocate general said the United Kingdom did not need the approval of the 27 remaining EU member states to halt the two-year countdown triggered invoking Article 50 of the Lisbon Treaty.
Downing Street insisted that it was "not a final judgment" and "does nothing in any event to change the clear position of the Government that Article 50 is not going to be revoked". Since most lawmakers oppose a no-deal Brexit, they could essentially take that option off the table.