In his first meeting with EU counterparts since his election victory earlier this month, Cameron said that "there will be lots of noise, lots of ups and downs along the way."
He has said that if Brussels refuses to budge on some essential demands, it could mean a so-called Brexit, the term for a potential British exit from the EU.
He kicked off his whirlwind campaign with several bilateral meetings at the EU-Eastern Partnership summit and will visit French President Francois Hollande Thursday and German Chancellor Angela Merkel next Friday.
Cameron has been insistent on regaining decision-making powers from the EU, specifically when it comes to immigration and justice issues.
Some EU leaders have acknowledged they share some concerns, but they have insisted that allowing people to travel freely across the EU's 28 nations remains a cornerstone of their policies, whatever the British objections.
Cameron said he realizes the way ahead will not be easy.
"You will hear one day this is possible and the next day something else is impossible," Cameron said. "But one thing throughout all of this will be constant and that is my determination to deliver for the British people a reform of the European Union."
French President Francois Hollande said it was up to Britain to do the heavy lifting if it wanted to push through change.
"We ask for nothing. Europe is not concerned by a vote," Hollande said.
