Merkel, speaking against the background of a planned reduction in corporation tax in Britain, also said EU members must agree on a joint approach to corporation tax.
"We all know that we need more harmonisation," she told a joint news conference with Luxembourg's Prime Minister Xavier Bettel.
Refering to Britain's decision to leave the EU and what looks like being a difficult and complex negotiating process on the divorce terms, Merkel said: "It is important that we do not allow ourselves to be divided, the 27 must act together in the negotiations."
The chancellor also stressed it was important for EU member states to increase the exchange of data to improve security in the bloc, and that they should quickly implement a register of people entering and leaving.
Since a Tunisian failed asylum seeker rammed a truck into a Berlin Christmas market, killing 12 people, last month before fleeing to Italy where he was shot dead, Merkel has stepped up her calls for cross-border cooperation on security issues.
"Everyone sees the urgency and everyone knows that if we do not succeed, each country will introduce its own border controls and free movement won't be possible," said Merkel, adding that meant freedom of services as well as of people.
"It makes me optimistic that a lot of countries have sadly had the experience that terrorism is a big challenge for all of us and only cross border cooperation in the (passport free) Schengen area will help us," she said.
(Reporting by Michele Land, Writing by Madeline Chambers in Berlin, Editing by Paul Carrel and Angus MacSwan)
