Jean-Claude Juncker and Donald Tusk made statements on the conclusions of last week's European Council meeting.
"A no-deal Brexit will never be our decision", Tusk said.
The European Council president told MEPs he was currently discussing British Prime Minister Boris Johnson's request for an extension with the leaders of the other 27 member states and would make a decision "in the coming days".
Tusk then paid tribute to Jean-Claude Juncker in the address, saying he admired his work despite not always agreeing.
"It was an emotional moment last week when I attended my last European Council," admitted Juncker, before getting straight to the perennially preoccupying concept of Brexit.
He branded Brexit negotiations as a "waste of time and a waste of energy," and expressed frustration as taking away time from his five-year mandate from making the bloc an entity that serves citizens better.
Juncker told the EU assembly in Strasbourg that they could only approve the Brexit deal once it had been approved by the British parliament.
"I will always regret the UK's decision to leave the union...but we have done all in power to prepare the EU for all eventualities" he went on, before adding that Westminster must ratify any Withdrawal Agreement before the EU does.
Johnson faces on Tuesday tow Brexit votes that will decide whether the UK leaves the EU on October 31.
European People's Party (EPP) group leader Manfred Weber said the EU had the "same right to do a proper assessment of the Brexit deal" than British parliament, adding it would be very difficult to reach a decision this week.
On the budget, Juncker asserted that the proposals by the Finnish president are not acceptable: "you cannot shape Europe with 1% GDP."
On enlargement, Juncker like Tusk called not opening accession talks with North Macedonia and Albania a "huge mistake".
The Socialists group leader Spanish MEP Iratxe García also condemned the move not to start accession talks with the two Balkan countries, saying their membership would "contribute to the stability in the region."
"This is a grave error because it affects these two countries in their heart," Juncker said.
As for Turkey's military incursion in Syria, it was Weber who condemned it the most, adding he was "disappointed" that the council "did not take more robust measures" against Turkey who he called an "aggressor".
"Turkey benefits from the customs union and the internal market and at the same, it's an aggressor," he said.