"The EU is strong enough to withstand Britain's withdrawal," she told parliament ahead of a crisis summit of the 28 member states in Brussels.
"It is also strong enough to successfully defend its interests in the world in future."
Expressing strong confidence in the union as it confronts the first defection since its founding, Merkel said the EU would continue to be a guarantor of "peace, prosperity and stability" in Europe.
"We will ensure there are no negotiations based on the principle of cherry-picking," she said to applause.
"There must be and will be a noticeable difference between whether a country wants to be a member of the European Union family or not."
She added: "Anyone wishing to leave this family cannot expect to lose all the obligations but keep the privileges."
Merkel also said access to Europe's common market depends on "accepting Europe's fundamental freedoms and the other rules and commitments that go with it".
A non-EU country can join the common market if its accepts the freedoms of people, goods, services and capital, she added, mentioning the example of Norway.
Merkel, who had huddled with the leaders of France and Italy yesterday in the aftermath of the shock referendum, said the three biggest economies on the continent had agreed on a "common position" on the approach to the Brexit vote.
She said she hoped the Brussels summit would take place in that spirit of unity, and said the EU's goal should aim to complete reforms of the bloc in time for the 60th anniversary of the Rome Treaty laying its foundations in March 2017.
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