Their talks were part of a conference at Chancellor Merkel's office in which Norwegian Prime Minister Jens Stoltenberg also took part. Ninety-three students were on hand as well.
The two leaders agreed that the EU's fiscal pact alone would not be able to stand alone as the only solution for the debt crisis threatening the eurozone.
"When we look at the medium and longer term, we need more coherence," Merkel said at a press conference following the meeting. "Not just in terms of fiscal policy, but also in other areas ... (the fiscal pact) is a necessary step, but not sufficient."
Merkel also said there were other points that needed to be addressed for the long-term future of the EU.
"For example, when one country spends nothing on research and another spends three percent of its gross domestic product, that cannot work in the long term," the chancellor said.
During the press conference, Cameron urged eurozone countries to take swift action to deal with uncertainty in the markets. He also made it clear that Britain - a country that is not part of the eurozone - expected the single currency bloc to handle the crisis, saying he could not call on British taxpayers to guarantee Greek or Spanish bank deposits.
Earlier in the day, Merkel appear on a morning talk show on German public television saying "more Europe" was the best way forward, meaning the future of the EU would lie in a closer political union that gives Brussels more authority.
"We don't only need a currency union, we also need a so-called fiscal union, that is, more joint budget policy," she said in an interview with German broadcaster ARD. "And we also need first and foremost a political union, meaning we must cede responsibilities to Europe step by step," she added.
Merkel acknowledged that the EU now has "different speeds," referring to the countries in the eurozone and those that have their own national currencies. She said the differences would become more pronounced over time, because the euro countries would inevitably draw closer together.
"We can't stand still because [others] don't yet want to come along," she said.
She said Europe should have a strategy for growth, but stressed that "budget consolidation and questions of growth are two sides of the same coin," adding that solid finances were necessary for growth.
Merkel has been the focus of increasing pressure domestically and internationally to find a solution to the eurozone financial crisis.
mz,ncy/pfd (AFP, dapd, dpa Reuters)