Guy Verhofstadt was speaking to his fellow MEPs on Monday at a constitutional affairs committee meeting in Parliament.
The Belgian deputy told MEPs that limited progress has been made after the first three rounds of Brexit talks, in particular, concerning the UK's financial commitments to the EU, otherwise known as its divorce bill.
During a lively debate, he expressed concern over the UK's attempts to question the exit bill and highlighted the importance of living up to previous economic commitments.
The meeting comes with EU leaders due to decide soon on whether sufficient progress has been made on divorce issues to move onto the future trading relationship.
Verhofstadt also acknowledged some positive developments in the field of safeguarding citizens' rights, for instance on healthcare, social security coordination and frontier workers.
But the MEP stressed that the British government's offer to provide EU citizens in the country with a 'settled status' is not acceptable, since it would cause a "tremendous administrative burden for a lot of people."
This proposal means, among other things, that all EU nationals lawfully resident in the UK for at least five years will be able to individually apply to stay.
The ALDE group leader also called for more clarity on the future of the border between the Republic of Ireland and Northern Ireland and underlined "the absolute need to avoid the current open arrangement being restricted."
His comments come with the UK saying it is seeking more regular Brexit negotiations with the EU. UK Prime Minister Theresa May's spokesperson said on Monday, "We are ready to intensify negotiations. Nothing has been formally agreed, but that is something that we can discuss. Typically in negotiations as time goes on you see the pace pick up.”"
The UK is proposing moving negotiations onto a rolling week-by-week structure.
In his presentation, Verhofstadt gave a comprehensive account of the latest developments and the progress made in the Brexit negotiations between EU and UK government officials, notably on citizens' rights. The talks opened on 19 June followed by a second round of negotiations in July and a third round last week.
This week, Parliament's Brexit steering group, chaired by Verhofstadt, will assess the UK position paper on Northern Ireland and Ireland, as well as other separation issues.
The European Parliament has already spelled out its conditions for approving the UK's withdrawal agreement. Any such agreement at the end of UK-EU negotiations will need to win the approval of a majority of MEPs.
On Tuesday, Parliament's Brexit steering group was expected to publish a comparative document containing the EU versus the UK position on citizens' rights.
Parliament's Conference of Presidents will soon start drafting a resolution to assess the state of play of ongoing talks between EU and UK government officials. This resolution is expected to be voted by plenary in October in Strasbourg.
Elsewhere, Martin Selmayr, chief of staff to European Commission President Jean-Claude Juncker, said that people who voted for Brexit made a "stupid" decision which could still be reversed by the British public.
Selmayr, speaking at a conference in Brussels on Monday, said, "Brexit is bad, and it's a stupid decision. The only people who can reverse it would be the British people and I am not a dreamer, I am a realist. Brexit will happen Brexit on March 29, 2019."
He said that while it was legally possible for the UK to reverse its decision, "it would be arrogant of us" to say the EU could force it to happen.