Manfred Weber was speaking after a one-day summit in Brussels on Thursday, where EU leaders discussed Brexit, due to start when the UK triggers article 50.
Weber, a German MEP who currently leads the EPP group, said: "The European Parliament should be fully involved in the negotiations between the European Union and the UK on Brexit."
Weber added, "Parliament will have the last word on the Brexit agreement. We call on EU leaders not to risk a 'No' from us on the final outcome of the negotiations. Parliament should therefore sit at the negotiating table from the start."
Also speaking after the summit, German Chancellor Angela Merkel said that Brexit was not yet an urgent task for the EU.
Even so, the issue was again near the top of the agenda for the summit, not least after Parliament President Martin Schulz gave a hardline warning ahead of the meeting that MEPs would not allow the assembly to be sidelined during the Brexit talks, due to commence next March.
Another issue on the summit programme was defence and the summit underlined the EU's aim to create a European defence union, which has been particularly championed by Jean-Claude Juncker, President of the Commission.
Commenting on the proposed defence union and plans for closer defence cooperation, the Co-Chair of the European Green Party Reinhard Bütikofer, welcomed the fact that EU leaders taken "serious steps to develop a genuine common defence policy since the Brexit decision."
The German deputy said, "The exit signal from the British that had long blocked such a development is now also proving as an aid to the further integration of the remaining 27 member states.
"With this, they now also finally react to the clear expectations of European citizens who have long been in favour of a stronger integration of European security policy."
Bütikofer also cautioned, "However, we have to warn against plundering all possible EU budgets for achieving the highest possible expenditure on armaments.
"It is not the problem of the European security policy that too little money has been spent on this. With a total of about €200bn a year, the EU member states jointly surpass Russia's military spending (almost €70bn) by about three times."
He explained, "Due to a strong fragmentation in procurement policy and a completely inefficient multiplication of the same abilities in several places, European armament spending has long been an outstanding example for the actual wasting of tax money.
"Therefore, efficient collaboration is the key."
As an example he said that in 2011 the army chiefs of EU countries had already identified 300 defence related projects but only in 19 of these had work started.
"Much stronger cooperation is also urgently needed in armament research, development and procurement - 80 per cent of the latter area is currently being taken care of at the national level."