Speaking after a crunch meeting with the leaders of Italy and France, Merkel insisted that Britain's vote on 23 June to leave the EU did not spell the beginning of the end for the European project.
After the meeting in Italy on Monday, the three leaders pledged to revive it by bolstering EU security, boost economic growth and give the continent's youth a future.
Merkel recalled that the EU had been borne from some of the "darkest moments" of European history but added that in the face of "enormous challenges" it must now work together, strengthening internal and external borders, boosting economic growth and providing jobs for its young people.
The talks were aimed at forging a common position as part of the three leaders' preparations for an informal summit in Bratislava next month of the 27 states that would remain in the EU after Britain leaves.
The leaders of the Eurozone's three biggest countries met on an Italian naval aircraft carrier and will now join other EU leaders and heads of state in Bratislava on 16 September.
Speaking after the informal get together, Merkel said, "We paid tribute to the roots of the European Union today and made clear with the laying of flowers on Altiero Spinelli's grave that we understand where this EU comes from and that it was born in Europe's darkest hour."
Merkel added, "We also know that it is our mission in the 21st century to guarantee people security while also respecting Europe's values."
"The goal must first of all be to preserve the status quo and to prevent a further disintegration of the EU-27," one EU diplomat was quoted as saying.
Italian Prime Minister Matteo Renzi hosted Merkel and French President François Hollande in an effort to prepare the groundwork for the Bratislava summit in September, which will not include the UK, to discuss the impact of Brexit.
"They came to discuss how to relaunch Europe from the bottom up, there's a big need," Renzi said.
"Many thought after the Brexit decision that Europe was finished. That is not the case," Renzi, said. "We will write the next page of our future."
Merkel is said to want "a better Europe" rather than continue with "more Europe," while Renzi is expected to push the EU to let Italy spend its way out of stagnation, even if that results in breaking the rules on deficit limits and is also keen on Italy having a strong voice in how the EU's future is moulded after Brexit.
Hollande reportedly pressed for an EU-wide investment plan to be doubled.
Separately, Renzi has said that there will be a new general election in 2018, no matter the outcome of his country's referendum on constitutional reform in October.
Asked in an interview whether elections would be held in 2018 whatever the outcome of the popular vote, Renzi said "yes".
He added "If the no [vote] wins I have already said what I will be doing," having previously stated he would resign.
Further comment came from Italian MEP Gianni Pittella, who leads the Socialist group in Parliament.
He said, "From the deepest crisis Europe has ever gone through and in front of all global challenges, the EU must relaunch its willingness to be together and react together.
"The Socialists and Democrats group urges a new beginning. It is imperative to start with new financial flexibility that finally overrides 'fiscal compact' and enables investments, growth and the creation of new jobs. The Juncker Plan 2 must be reinforced and relaunched, as well as prioritising the social pillar.
"A reunited Europe must definitely start from the full implementation of a common migration policy. It is high time all member states take a decisive step towards solidarity, thereby enabling the EU to be effective in welcoming migrants whilst fighting the root causes of migration."