Video report by ITV News Political Correspondent Paul Brand
David Sassoli said the European Union fully expects the UK to "honour the commitments" which were signed up to last year when the UK and EU negotiated the Withdrawal Agreement, "especially with regard to citizens' rights and Northern Ireland".
"Any attempts by the UK to undermine the agreement would have serious consequences," he said.
Mr Sassoli said if the UK reneges on the agreement that it signed up to last year, "then trust and credibility will be lost".
He added: "In 114 days, EU law will no longer apply in the UK.
"Time is not on our side and frankly, I am deeply worried considering the lack of progress in the negotiations at this late stage."
The comments come amid proposals by the government to implement a domestic law - the Internal Market Bill - which aims to ensure goods from Northern Ireland continue to have unfettered access to the UK market while making clear EU state aid rules – which will continue to apply in Northern Ireland – will not apply in the rest of the UK.
Europe Editor James Mates gives the reaction in Germany
Earlier, Northern Ireland Secretary Brandon Lewis admitted the UK would “break international law” if it follows through with the proposals.
Mr Lewis told MPs it would be in a “very specific and limited way”, adding there are “clear precedents” for the UK and other countries which need to consider their international obligations as circumstances change.
His Labour counterpart Louise Haigh described the admission as “absolutely astonishing” and warned it would “seriously undermine” the UK’s authority on the international stage.
Mr Lewis told MPs the Government is “fully committed” to implementing the Withdrawal Agreement and the Northern Ireland protocol.
But he added the UK is taking “limited and reasonable steps to create a safety net” to allow it to deliver on its commitments to the people of Northern Ireland and keep in line with the protocol should outstanding issues not be resolved in talks with the EU.
Conservative Sir Bob Neill, chairman of the Justice Select Committee, later asked: “The Secretary of State has said that he is committed and the Government are committed to the rule of law. Does he recognise that adherence to the rule of law is not negotiable?
“Against that background, will he assure us that nothing that is proposed in this legislation does or potentially might breach international legal obligations or international legal arrangements that we have entered into?”
Mr Lewis replied: “I would say to (Sir Bob) that yes this breaks international law in a very specific and limited way.
“We are taking the power to dis-apply the EU concept of direct effect required by Article 4 in a certain, very tightly-defined circumstances.”
He added that “there are clear precedents for the UK and indeed other countries needing to consider their international obligations as circumstances change”.
Tory former party leader Iain Duncan Smith said the Government was “quite within its rights” to revisit the Withdrawal Agreement.
Earlier it was reported how the head of the UK's legal department, Sir Jonathan Jones, had quit over the proposals.
Downing Street confirmed that Sir Jonathan had resigned as permanent secretary of the government Legal Department but would not comment on the reason for the departure.
The Prime Minister's official spokesman said: "I can confirm that he is stepping down and we would thank him for his years of hard service and wish him well for the future."
Critics of the move to override the Withdrawal Agreement have said it would breach international law if the UK reneged on its agreement.
Ursula von der Leyen, President of the EU Commission said the Withdrawal Agreement is a "prerequisite for any future partnership" and suggested there will be no trade deal if the UK does not stick to its side of it.
Former prime minister Theresa May suggested the move to backtrack shows the UK cannot be trusted to uphold international agreements.
In the Commons, during a Urgent Question debate on the Northern Ireland protocol, Ms May criticised the move.
She said: "The UK government signed the Withdrawal Agreement with the Northern Ireland protocol - this Parliament voted that Withdrawal Agreement into UK legislation.
"The government is now changing the operation of that arrangement.
"Given that, how can the government reassure future international partners that the UK can be trusted to abide by the legal obligations of the agreements it signs?"