Michel Barnier has called on Theresa May to shift her focus from renegotiating the Irish backstop to one that embraced a closer relationship with the EU to secure cross-party support for the Brexit deal.

While the prime minister stated her intention in parliament to plough on with seeking concessions on the withdrawal agreement, the EU’s chief negotiator suggested this was no longer a “key part of the debate” in the UK.

“As I see, following carefully the political debate in London … this debate is much more now on the future relationship between the EU and the UK,” Barnier said as calls grow for May to move closer to Labour’s position on a permanent customs union. “It’s now for the UK leaders to build this stable and political majority for a deal. We are waiting for the next steps and are ready to work again on the political declaration.”

The intervention echoed the comments of Peter Altmaier, Germany’s economics minister and a key ally of Angela Merkel, who appeared to warn both Labour and the Conservatives against abandoning their cross-party talks.

“Sympathy, patience and readiness to wait until the UK’s position will be clarified are of utmost importance to avoid the worst,” he tweeted. “They should not be misused for party politics. Large majority wants to exclude hard Brexit – in the interest of the UK and beyond.”

The European parliament’s Brexit coordinator, Guy Verhofstadt, welcomed May’s announcement to waive the £65 fee for EU nationals applying for settled status, but added: “I hope cross-party cooperation and consultations will really start now.”

May’s statement in the Commons in which she set a target of securing a time limit on the backstop was seen in Brussels as an attempt to placate the Democratic Unionist party and the Brexiters in her own party, but there are severe doubts among EU leaders about the stability of such a parliamentary coalition.

Before the statement, Spain’s foreign minister, Josep Borrell, said the scale of defeat for May’s Brexit deal last Tuesday, by 230 votes, suggested she would need to rethink her strategy. “I think that such a large difference in votes, we are talking about a 1:3 ratio, such a big difference, I do not think it can be saved with marginal adjustments in the current plan,” he said.

“I do not think she can convince MPs by presenting the same agreement with some tweaks.She has to bring something substantially different but, of course, that would have to be approved by the EU, so we have to wait until this afternoon to see what she says.”

Borrell said parliamentary support was essential. “We cannot continue negotiating something, as it has happened this time, and when everything is negotiated, the parliament rejects it,” he said. “We have to have the guarantee that she has enough political support so that what is negotiated is not rejected at the last moment.”

Jean Asselborn, Luxembourg’s minister of foreign affairs, openly voiced his hope Downing Street could still move towards a permanent customs union.

Jacek Czaputowicz, Poland’s EU affairs minister, suggested a five-year time limit on the backstop could solve the problem in a break from the rest of the bloc. “Of course, this would be less beneficial for Ireland than an indefinite backstop, but much more favourable than the no-deal brexit, which inevitably approaches,” he said.

Czaputowicz, whose country is at loggerheads with the European commission over its judicial reforms at home, further claimed the EU had become a hostage to Ireland’s demands over the border.

“Probably [the Irish] thought that the United Kingdom would at some point agree to an indefinite backstop, which did not happen,” he said. “And now we have a game of a coward, two cars are running on each other and we will have a frontal collision.”

Germany’s foreign minister, Heiko Maas, said “nerves are raw” about the threat posed by Brexit to peace on the island of Ireland, after a car bomb exploded outside a Derry police station on Saturday.

He said the Irish backstop, which would guarantee the avoidance of a hard border by keeping the whole of the UK in a customs union until a satisfactory arrangement was in place, was “a topic where I can only see little changes being made during the negotiations and talks”.

Following a meeting with Barnier, Ireland’s deputy prime minister, Simon Coveney, added that the Polish minister’s suggestion did not reflect the EU’s thinking. “I think the conversation I had with Michel Barnier today pointed to the willingness of the EU to be flexible in the context of the future relationship declaration.” Coveney said. “I hope we will see a willingness to look again perhaps at the future relationship that Britain is seeking with the EU as a mechanism to find a way forward.”