Incoming UK PM Boris Johnson faces "challenging" times, the EU has warned, as it reacted to his election as new Conservative leader.
Mr Johnson has the immediate task of guiding the UK out of the EU ahead of a 31 October deadline.
He says he wants to renegotiate an agreement with the EU, ditching large parts of the deal outgoing PM Theresa May struck last year.
But EU leaders have said the withdrawal agreement is not up for renegotiation.
The European Commission's newly elected President, Ursula von der Leyen, has however said she is willing to grant the UK another extension to Brexit talks, if London comes up with good reasons.
Congratulating Mr Johnson, Mrs von der Leyen said: "There are many different and difficult topics to tackle together. There are challenging times ahead of us. I think it is very important to build up a strong and a good working relation because we have the duty to deliver something that is good for people in Europe and in the United Kingdom."
The EU's Brexit negotiator, Michel Barnier, is due to meet MEPs on the European Parliament's Brexit Steering Group in an extraordinary meeting on Wednesday to respond to Mr Johnson's election.
US President Donald Trump meanwhile congratulated Mr Johnson on his victory, tweeting:
Congratulations to Boris Johnson on becoming the new Prime Minister of the United Kingdom. He will be great!— Donald J. Trump (@realDonaldTrump) July 23, 2019
Later, he said: "We have a really good man is going to be the prime minister of the UK now, Boris Johnson. A good man. He's tough and he's smart. They're saying 'Britain Trump'. They call him 'Britain Trump' and people are saying that's a good thing. They like me over there.
"That's what they wanted. That's what they need... He'll get it done. Boris is good. He's going to do a good job."
In the often divisive Brexit world of "them and us", it is easy to forget that, beyond Brexit, EU leaders still see the UK as a close partner and ally.
Tuesday's messages of congratulation to Boris Johnson from across Europe were a timely reminder.
Whatever happens with Brexit, France, Germany, Poland et al still very much hope to work closely with the UK on international issues like Russia sanctions, Iran and human rights protection.
But EU leaders' welcoming tone does not signal a willingness to accept whatever Prime Minister Johnson might demand in terms of changes to the Brexit deal.
He's right when he says a no-deal Brexit is bad for Brussels, but he overestimates EU wiggle room. Amendments will only be forthcoming if EU leaders deem them workable and are convinced the new prime minister commands a majority in parliament to get the Brexit deal through once and for all.
There has been further reaction across Europe:
In Germany, Chancellor Angela Merkel congratulated Mr Johnson, saying she would keep pursuing a "strong friendship" with London.
"I congratulate Boris Johnson and look forward to good co-operation. Our countries should continue to share a strong friendship in the future."
In a statement, her CDU party said they expect Mr Johnson "to pursue a responsible policy in Britain's interest. Responsible means - even for a Brexit hardliner - to prevent an unregulated Brexit at all costs".
German industry chiefs have also warned of the dangers of no-deal Brexit. Joachim Lang, CEO of the Association of German Industry, said: "Threats from London to leave the EU with no deal are harmful and will come back like a boomerang. They exacerbate damages that have already affected the economy."
Mr Johnson has pledged the UK will leave the EU on 31 October "do or die", accepting that a no-deal exit will happen if a new agreement cannot be reached by then.
France's President Emmanuel Macron praised outgoing Prime Minister Theresa May's "courage and dignity" and the fact that she had never "blocked the workings of the European Union".
On the new man in charge, he said: "I am looking forward to working with him, not only on European topics and the ongoing Brexit negotiations, but also on important international topics... such as Iran and international security."
Italy's Interior Minister and leader of the Lega (League) party, Matteo Salvini, tweeted: "Good job #BorisJohnson. The fact that on the left they depict him as 'more dangerous than the Lega' makes me like even him more."
The EU's chief Brexit negotiator Michel Barnier tweeted:
We look forward to working constructively w/ PM @BorisJohnson when he takes office, to facilitate the ratification of the Withdrawal Agreement and achieve an orderly #Brexit. We are ready also to rework the agreed Declaration on a new partnership in line with #EUCO guidelines.— Michel Barnier (@MichelBarnier) July 23, 2019
The deputy prime minister and foreign minister of Ireland, Simon Coveney, tweeted:
Congratulations to @BorisJohnson on becoming leader of the UK Conservative Party - we will work constructively with him and his Govt to maintain and strengthen British/Irish relations through the challenges of #Brexit 🇬🇧🇮🇪🇪🇺— Simon Coveney (@simoncoveney) July 23, 2019