Angela Merkel has said she is "not frustrated" by the Brexit process but is "curious" to know more about the UK's aims after meeting Theresa May.
The German chancellor said she hoped to establish "common ground" on future trade goals in the coming months and wanted a "close partnership" of equals.
Mrs May said she wanted a "bold and ambitious" trade partnership as well as a new security arrangement with the EU.
But amid calls for more UK detail, she said it was not a "one-way street".
Friday's meeting between the two leaders at Berlin's Chancellery comes ahead of a speech on Saturday in which Mrs May will set out the "security partnership" she envisages with European partners at the annual Munich Security Conference.
Theresa May has called for a new "deep and special partnership" to ensure the UK and EU can continue to work together on security after Brexit.
She said new arrangements in foreign and defence policy cooperation should be effective by next year.
In a speech to the Munich Security Conference the prime minister said the UK would remain committed to Europe's security after leaving the EU.
Mrs May has had a busy couple of days meeting Merkel on Friday, then her snow bound speech in Munich yesterday, but are we any the wiser where the government is taking us with regards to Brexit?
The Europeans keep saying they want details, I'm beginning to agree with them!
Will May use security as a negotiating tactic in the upcoming negotiations? It certainly sounded like she was putting that on the table and that's what Juncker thought as well with his trite comments after her speech.
Be glad when Brexit is done and dusted!