The Parliament's chief Brexit negotiator, Guy Verhofstadt, has held talks with David Davis, the UK's Brexit secretary.
Verhofstadt, who chairs the Parliament's Liberal ALDE group, said the meeting was "not a negotiation", but rather a "first formal contact" for the two men.
The Belgian MEP said that during the talks, he reiterated "three essential key points".
The first of these was that "in the interest of everyone", the negotiations should be concluded before the 2019 European elections. "It would be very strange," argued Verhofstadt, "if the UK had to organise elections for the European Parliament after the outcome of the Brexit vote."
And, he added, "this would provide a fresh start for a new legislative period."
The second key point, said Verhofstadt, was that "there has to be a close partnership with the EU and UK, not so much in the interests of those involved in the negotiations, but in the interests of UK and EU citizens.
"In that respect, I underlined the necessity to work on a reformed, more effective EU, different from today's Union, with less complexity."
According to Verhofstadt, beyond "starting and concluding Brexit", for the remaining EU 27, the discussions will also be about "the EU that will emerge in the next few years."
The third key point the former Belgian Prime Minister raised with David Davis was that of the EU's four freedoms, saying, "It is impossible to find solutions where we destroy the four freedoms - the are a basic element of the EU and I will certainly never accept a development that puts them at risk." This, said Verhofstadt, was also the position of the Commission and Council.
The four freedoms are the movement of goods, services, people and capital. Immigration played a pivotal role throughout the Brexit referendum campaign, with UK policymakers calling for tighter controls on immigration. However, decision-makers on the EU side have warned that the UK would not be granted access to the single market without accepting freedom of movement.
Verhofstadt also warned that the window for negotiations was small, "more or less 14-15 months" and reiterated that the European Parliament would have to ratify any deal. "It's going to be a tough and very intense period."