The EU has urged Liz Truss to respect the Brexit agreement, as it called on the incoming British prime minister to take a broader view of Britain’s relationship with Europe.

The European Commission president, Ursula von der Leyen, who is expected to speak to Truss by phone in the coming days, tweeted her congratulations, referring to common challenges, from climate change to the Russian invasion of Ukraine.

She said: “I look forward to a constructive relationship, in full respect of our agreements.”

Maroš Šefčovič, the EU’s top official in charge of relations with the UK, said a positive relationship between the two was of great strategic importance. “I stand ready to work intensively and constructively with my new UK interlocutor to foster such a partnership, in full respect of our agreements.”

The French president, Emmanuel Macron, also congratulated Truss, stating that “the British nation is our ally”, a few weeks after Truss told Tory members at a hustings event in August that she was undecided as to whether he was “friend or foe” when asked.

“Congratulations to Liz Truss on her election,” Macron tweeted. “The British people are our friends, the British nation is our ally. Let us continue working together to defend our shared interests.”

Behind the scenes, EU officials have low expectations of an improvement in relations with Truss, the architect of a bill to override key aspects of the Northern Ireland protocol, which could lead to a trade war.

“The wish on this side is for things to improve, for there to be a more constructive relationship, but I don’t think anybody is holding their breath,” an EU diplomat said.

The diplomat suggested that Truss’s reliance on Eurosceptic MPs in the Conservative parliamentary party did not bode well for her ability to strike compromises. They added: “Looking at where Liz Truss got her support I don’t really expect her to have that much room for manoeuvre. But I would gladly be proved wrong.”

Sources hope that once installed in No 10, Truss will take a different tack to EU relations.

“Obviously the reservations that were there beforehand remain given that she was the foreign secretary that brought through the [Northern Ireland] bill before the summer,” one EU diplomat said. “From an EU perspective, there is always a window of opportunity with the new prime minister, because the EU will be open to talks and negotiations.”

Nathalie Loiseau, a French MEP who co-chairs the EU UK parliamentary partnership assembly, said she wished Truss the best of luck “because the success of the UK is important for its allies and neighbours”. Loiseau, a former Europe minister, added: “I hope she will refrain from making things more difficult between the EU and the UK and engage in a strong partnership.”

David McAllister, a German centre-right MEP, who chairs the European parliament’s foreign affairs committee, congratulated Truss, while pointing to the agreements the British government had signed. He said: “The EU is keen to have stable and positive relations with the United Kingdom based on our agreements, mutually negotiated, signed and ratified by the EU and the UK. Facilitating the practical implementation of the protocol on Ireland and Northern Ireland is of key importance.”

The German chancellor, Olaf Scholz, was one of the first leaders to offer his public congratulations, in a tweet that avoided mentioning the UK-EU dispute. He said: “I am looking forward to our cooperation in these challenging times. The UK and Germany will continue to work closely together – as partners and friends.”

Truss, who will become prime minister on Tuesday, will be tested on her openness to work with the EU when she is invited to join European leaders for a summit in October. She will be invited to discuss the creation of the European Political Community, a pan-European body dedicated to promoting security and other ties among the nations of Europe.

Her elevation to 10 Downing Street was given short shrift by the Kremlin, which said dire relations with Britain could get even worse. “I wouldn’t like to say that things can change for the worse, because it’s hard to imagine anything worse,” the Kremlin’s spokesperson Dmitry Peskov replied when asked if Moscow expected any shift in relations with Britain, Reuters reported.

“But unfortunately, this cannot be ruled out.”

In Moscow, Truss is best known for her February meeting with the Russian foreign minister, Sergey Lavrov, who complained that her interventions were “just slogans shouted from the tribunes”.

In the meeting, which took place two weeks before the Russian invasion, Truss challenged Lavrov on the buildup of 100,000 troops on Ukraine’s border, which Moscow denied was preparation for an attack. She was also mocked by the Russian government for confusing Russian regions with Ukrainian territory and apparently mixing up the Black and Baltic Seas.

Truss received a warmer reaction from the UK’s traditional allies. In a statement of congratulations, New Zealand’s prime minister, Jacinda Ardern, referred to New Zealand’s “exceptionally strong relationship with the United Kingdom based on our shared values, history and culture”.

In her roles as trade and then foreign secretary, Truss was “a staunch supporter of the UK’s ‘tilt’ to the Indo-Pacific and played a central role in advancing our historic free trade agreement” Ardern said.

Gibraltar’s chief minister, Fabian Picardo, praised Truss’s role in negotiations over the post-Brexit future of the British overseas territory, which voted to remain in the EU.

“Liz was instrumental in delivering trade deals for Gibraltar and as foreign secretary we have worked very closely together on all issues, not least on the negotiations for a UK/EU treaty on Gibraltar’s future relationship with the EU,” he said.