The visit marked a further step in "lending dynamism to our friendly relations," the chancellor said after talks with President Abdelaziz Bouteflika.
Although only one major contract was signed -- for the building of a huge mosque capable of holding 40,000 worshippers -- business leaders travelling with Merkel expressed hopes for further deals.
During the visit, a working group with business leaders and government representatives from both sides was established to promote economic ties. German companies have their eye on Algeria's large foreign exchange reserves and on the large reserves of oil and natural gas.
The mosque contract, to build the world's third-largest mosque in Algiers, was signed during the visit.
German architects Engel and Zimmermann, together with construction engineers Krebs and Kiefer, are to build the mosque costing 1 billion euros ($1.6 billion) over the next four years after winning the contract last year.
Among other contracts under consideration is the delivery of four German-built frigates to the Algerian navy at a cost of some 5 billion euros.
Doing more business
Mutual trade between Germany and Algeria was running at 1.2 billion euros in 2007.
"We can increase this and want to do so," Merkel said.
Ekkehard Schulz, board chairman of steelmaker ThyssenKrupp, predicted a rise in mutual trade, with North Africa becoming an increasingly important region for Germany.
ThyssenKrupp, in alliance with other companies, was working on building one of the world's largest fertilizer plants in Algeria, he said.
German energy companies E.ON and RWE are interested in oil and gas contracts, and there are plans for a combined gas and solar energy electricity generation plant. Germany is among world leaders in solar technology.
The visit came just three days after the launch in Paris of the Union for the Mediterranean, a programme to bind the nations of Europe and North Africa that was devised by French President Nicolas Sarkozy.
On Thursday, Merkel used the occasion of her 54th birthday to express support for the women of Algeria in their fight for equal rights.
Merkel met Algerian women working in science, the arts and the media. Women in Muslim countries would follow their own course, Merkel, herself a scientist by training, said, but she stressed that family law and the protection of women's rights had to be developed.
Merkel had originally planned to fly back to Berlin in time for an evening birthday celebration with friends in the German capital. But after a mobile gangway crushed into her plane and ruptured it, the chancellor's return flight was delayed.
Because of that, Merkel extended lunch and a coffee break with Bouteflika, who offered her a replacement plane from national Air Algerie, which first had to be prepared for take-off. Merkel's own plane, named Theodor Heuss after Germany's first president, was to fly back without passengers after rudimentary repairs.