Tusk said he was "ready for this judgement" by the 28 leaders but rejected criticism by Poland's right-wing prime minister Beata Szydlo that he had "brutally violated" his job's supposed political neutrality.
Szydlo did not clarify how she would cooperate with Tusk in the future, but said she would also participate in Friday's informal meetings regarding the Rome summit on the future of Europe.
Jarosław Kaczyński (C) is the leader of the ruling party in Poland.
The first task for the leaders on Thursday, when they will meet at 28 with Britain included, will be deciding on a new term for Tusk until the end of 2019.
"Nothing without us, without our consent", Szydlo said upon arrival for the summit.
Malta now holds the European Union presidency, and its deputy prime minister, Louis Grech, said negotiations were underway on the new head of the council.
But Malta's prime minister, who will preside over the vote, indicated that there's little appetite for a delay.
Warsaw argued that the decision should be delayed.
"The main objective must be to reconnect the European Union to people and make it worthy of their trust by being more respectful to its member states, focused on where it can add value", he added.
After being confirmed as president again, he tweeted: "Grateful for trust & positive assessment by #EUCO (European Council)".
Tusk was prime minister at the time.
"There is an overwhelming support for President Tusk's re-election", Joseph Muscat told reporters.
The Polish government, headed by the conservative Law and Justice Party, has instead nominated European Parliament member Jacek Saryusz-Wolski, who was kicked out from Tusk's Civic Platform party this week for accepting the offer to challenge Tusk. "I don't see how one country could oppose this solution when all the others are in favour", said Hollande as he arrived for the summit, quoted in the Associated Press. "The EU will remain engaged in the Western Balkans and stand by its commitments", Tusk said. But Mr Tusk is still expected to get enough support to keep his post.