Speaking in front of Merkel and others at Cebit, a world-leading information technology trade fair in Hanover, Abe asked the German leader to "walk alongside" him in the effort.
"At a time when we are arguing a lot over free trade, open borders and democratic values, it's a good sign that Japan and Germany are not arguing" over trade, she said.
The German and Japanese leaders were both coming off a week of meetings with U.S. President Donald Trump's administration.
He added: "Of course to do so it will be necessary to have rules that are fair and can stand up to democratic appraisal".
The Japanese Prime Minister, in Germany as part of his European tour, echoed that sentiment and expressed hope for a free trade deal to be struck between the EU and his country.
G7 leaders meet in Italy in May and trade is likely to be one of the thorniest issues at the table.
Merkel stressed that Germany was strongly in favor of free trade and open markets. "That's what free trade is about", she said.
Both called for a free trade deal to be reached quickly between Japan and the European Union, in comments made after G20 finance ministers and central bankers dropped a long-standing mention of open trade in their final communique after a two-day meeting in Germany.
"Of course, the views are different and this will not change through one meeting", Merkel said of differences with the USA administration on trade issues that surfaced during her talks with Trump in Washington last week. He was among those in the audience for the news conference.
Trump insisted he was not isolationist, saying: "I'm a free trader but also a fair trader". Europe "must never retreat, wall itself off or withdraw", she said in a speech to parliament in Berlin on March 9.
Germany is ready to "be the motor" for completing the deal as a signal that "we want free, open markets", Merkel said Sunday.