The two MEPs also emphasised that any withdrawal agreement concluded will require the approval of Parliament to take effect.
Parliament President Tajani said, “Parliament's position is clear. Preserving the rights of the millions of EU citizens affected by Brexit, securing the achievements of the Good Friday agreement for Northern Ireland and honouring the financial commitments made by the British government will be indispensable in securing the European Parliament's approval of a potential exit deal.”
The Italian EPP group deputy said, “Negotiations detailing the UK's withdrawal from the EU must now begin in earnest, and I expect that they will be conducted in an orderly manner and in a spirit of cooperation."
His comments were echoed by Verhofstadt, Parliament’s Brexit coordinator.
The Belgian deputy said, "I am glad that we are sticking to the negotiating timetable which is already quite tight. Let's now, first of all, make progress in the field of citizens' rights and create legal certainty for both our people and our companies."
In April, Parliament, by an overwhelming majority, adopted a resolution outlining its priorities and conditions for the negotiations on the withdrawal of the UK from the EU.
On Monday, a Parliament spokesperson told this website that the assembly’s Brexit priorities included giving an “absolute priority to fair and equal treatment” for EU and British citizens.
He also stressed that the UK will need to meet all of its financial commitments, including those that may run beyond the withdrawal date.
In the resolution MEPs emphasised that the EU's four freedoms - of goods, capital, services and people - are “indivisible” and any transitional arrangement must not last longer than three years.
The parliament source said that any deal on the future framework could involve cooperation on a variety of issues, ranging from defence, the fight against terrorism, the environment, research and education.
One of the key issues would be to agree the basis for future trade, including possible tariffs, product standards and how to resolve disputes.
Michel Barnier, who started the Brexit talks on Monday with David Davis, the Secretary of State for Exiting the EU who heads the UK side, has stressed a number of principles for the negotiations, including that EU membership must always remain the most advantageous status and any new relationship must be based on a “level playing field.”
If there is no deal and there is no agreement on extending the deadline, then the UK automatically leaves the EU after the two-year period. In addition, if no agreement is reached on trade relations, the country would have to trade with the EU under WTO rules.
The withdrawal agreement cannot enter into force without the consent of Parliament and, in the coming weeks, MEPs are expected to adopt a resolution setting out the red lines for the Parliament.