Tory and DUP MPs forced the Exiting the EU Committee to publish rival recommendations within the official text that was backed by the majority of members.
Prominent Conservative Jacob Rees-Mogg attacked the "high priests of Remain" for pushing through a "partisan" report.
Labour chairman of the Exiting the EU Committee Hilary Benn said the divisions showed achieving an agreement on Brexit "is far from easy".
The committee called for a provision in withdrawal arrangements to allow the transition period to be extended "if necessary".
Mr Benn said: "We are now at a critical stage in the negotiations, with just seven months left to reach agreement on a whole host of highly complex issues.
"While the committee welcomes the progress that has been made in some areas, the Government faces a huge task when the phase two talks actually begin.
"The Government must now come forward with credible, detailed proposals as to how it can operate a 'frictionless border' between Northern Ireland and the Republic of Ireland because at the moment, the committee is not persuaded that this can be done at the same time as the UK is leaving the single market and the customs union.
"We know of no international border, other than the internal borders of the EU, that operates without checks and physical infrastructure. This is deeply concerning."
Brexit Secretary David Davis has said he can "live with" a transition period of under two years if it helps to secure an early deal.
Mr Benn said: "But even this time could prove to be too short to conclude a comprehensive agreement. Given the modelling we have seen, a 'no deal' scenario is a significant danger to the UK."
The committee split on a series of votes over the content of its report on the progress of withdrawal negotiations.
Mr Rees-Mogg and fellow Conservatives Sir Christopher Chope, Andrea Jenkyns, Craig Mackinlay, and John Whittingdale, along with the DUP's Sammy Wilson refused to sign off the final version.
They used parliamentary procedures to ensure a "minority" report was included in the publication of the main text, a move rarely used.
Committee member Mr Rees-Mogg, chairman of the Brexit-supporting Tory European Research Group, said: "The committee's majority report is the prospectus for the vassal state. It is a future not worthy of us as a country, and I am sure that Theresa May will rightly reject a report by the High Priests of Remain.
"The majority report would keep us in the customs union and the single market which is an attempt to keep us in he EU by sleight of hand. Those of us who respect the instructions the people gave us in the referendum could not support so partisan a text.
"The majority report relies upon discredited economic models and makes no acknowledgement of past analytical failures. It appears to have been written in the slough of despond, despairing and defeatist."
The report said 21 months is "ample" time and warned a prolonged transition period "would be difficult for the UK and would not respect the referendum result".
It says the UK would still be bound by EU rules and would have to hand over cash with no say on how it is spent if the implementation arrangements are extended.
Mr Whittingdale, vice chairman of the committee, said: "I am very disappointed that the committee was unable to produce a unanimous report and instead divided along the same lines as in the referendum campaign.
"For a number of us the chairman's report was far too negative and we do not believe that its conclusions are borne out by the evidence we heard. The report's recommendations essentially ignore the wishes of the people and would delay Brexit by an indefinite period.
"This disrespects the referendum result, and it ignores the manifesto commitments of the parties pledged to honouring it, who between them got more than 80% of the popular vote."
The Department for Exiting the European Union insisted a "great deal of progress" had been made since the negotiations began last year, including securing citizens' rights, agreeing a financial settlement and setting out the approach to the Northern Ireland border.
"Importantly, the UK and the EU are equally committed to ensuring that our departure does not lead to a hard border between Northern Ireland and Ireland," a spokesman added.
"We are currently discussing the terms of an implementation period and are confident we can reach an agreement by the European Council next week. Doing so will provide businesses and citizens with the certainty they need as we prepare for exit.
"It remains a shared aim to get the withdrawal agreement agreed by October and we will continue to work closely with the commission to achieve that."