Merkel and Cameron conferred after tension between the two countries arose over how to stabilize Europe's economy, CNN reported.
"The United Kingdom has a great interest, and very sensibly so, in seeing the eurozone being strong," Merkel said.
Although the two nations have different opinions on how to boost competitiveness, Merkel said, Britain and Germany are tied by "strong bonds of friendship."
Cameron is lobbying for a deal, reached at a summit in Europe on Oct. 27, to be implemented as soon as possible. The deal calls for a series of measures to be taken to address the debt crisis in Europe, including debt relief for Greece, new capital requirements for banks and a plan to build financial safeguards around fragile euro area economies.
"A strong, successful and stable eurozone is in all our interests," Cameron said. "We need this crisis to be resolved. Britain, like Germany, has a big national interest in that happening."
Although the two countries did not make progress on the European financial transactions tax, they did agree a global tax would be OK, The Daily Telegraph reported.
Cameron said he and Merkel were in "absolute agreement" on tying European budget growth to inflation, the need for deficit reductions and boosting competitiveness and deregulation in the European market.
"It's obvious we don't agree on every aspect of European policy," Cameron said. "Germany has her interests and so does Britain. ... We've agreed to work together to achieve our respective interest."
In a joint statement, Cameron and Barroso said they agreed "on the importance of prioritizing the decisive action needed to ensure the stability of the euro area, as well as fast-tracking measures to stimulate growth and jobs."
Meanwhile, credit rating agency Fitch warned Italy is probably in a recession but Greece's budget forecasts were better than expected.
"Italy is likely already in recession and the downturn in activity across the eurozone has rendered the task of the [country's new emergency] government much more difficult," the ratings agency said in a statement.
Fitch downgraded Italy to A-plus from AA-minus last month.
Greece's 2012 deficit is expected to drop to 5.4 percent of the gross domestic product from 9 percent this year, the Telegraph reported. It previously was forecast to drop to 6.8 percent.