EU President Donald Tusk warned Monday that negotiations on reforms demanded by Britain ahead of an in-out referendum are "fragile" and have reached a "critical moment," amid a whirlwind of diplomacy to win over other member states.

Fears are rife that Britons might vote to leave the European Union, destabilizing the bloc politically and economically - and at worst starting to tear it apart.

EU leaders will attempt later this week to strike a deal on the reforms, which British Prime Minister David Cameron has said would allow him to campaign for his country to remain an EU member. He has promised to hold the referendum by the end of 2017.

Cameron and Tusk are both touring European capitals this week in a bid to drum up support for the reforms on immigration, competitiveness, economic governance and sovereignty. Tusk has prepared a compromise package for the leaders, but is facing resistance in some countries.

"The risk of break-up is real because this process is indeed very fragile," Tusk said on Monday evening after talks in Bucharest with Romanian President Klaus Iohannis.

He warned that "what is broken cannot be mended" and urged EU leaders to start "listening to each other's arguments more than to our own."

Iohannis stressed that in-work benefit restrictions negotiated by Britain cannot last indefinitely and must not be discriminatory. Romania is one of the countries with particular concerns as many of its citizens live and work in other member states.

Romanian Prime Minister Dacian Ciolos also insisted during a visit to Brussels that any special mechanism granted to Britain for in-work benefits should be "applied only in exceptional cases ... for a time period the most brief possible."

There are concerns in other EU member states too about different aspects of the deal being considered for Britain. France for instance has raised concerns about London's quest to prevent decisions taken by the 19-country eurozone from harming its interests.

French politicians have also repeatedly rejected British demands. Last week, Prime Minister Manuel Valls said that the EU did not need an additional crisis, adding that, as a member state, Britain could not "dictate its conditions."

Tusk visited Paris on Monday afternoon for talks with French President Francois Hollande.

An EU source, who spoke on the condition of anonymity, described the meeting as "good" and said that there was "progress." However, there is "still more work to do," the source said.

Later in the evening, Hollande met with Cameron at the Elysee Palace. The British demands for incentives to stay in the EU were expected to dominate their talks, which were billed as a chance for the two to prepare for the leaders' summit later this week.

The shuttle diplomacy will continue on Tuesday, with Tusk due to visit Greece, the Czech Republic and Germany, where he will hold talks with Chancellor Angela Merkel.

Cameron, meanwhile, will be in Brussels for meetings with European Parliament leaders and European Commission President Jean-Claude Juncker.

"We do have to approach this question of the social welfare system with a maximum of prudence," Juncker told journalists in Brussels on Monday after meeting with Ciolos.

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