LONDON—European leaders criticized U.K. Prime Minister David Cameron's promise to renegotiate his country's relationship with the European Union and let the British people vote on the outcome, creating potential hurdles to his plan.

"The EU does not need unwilling Europeans," said Mario Monti, Italy's prime minister and a former European commissioner, during a speech at an annual meeting of political and business leaders in Davos, Switzerland. "We need more, not less integration," German Foreign Minister...