Merkel stressed the central role of Egypt as an anchor of stability in a conflict-torn region, referring to the Islamic State jihadist group fighting in Iraq and Syria, instability in Libya and Nigeria's Boko Haram militants.
"Egypt is one of the central countries in a region marked by unrest and instability," the chancellor said, adding that closer business links would help bring "stability through economic development" in the North African country.
Sisi's visit to Berlin was greeted with military honours by the government, but also angry protests on the streets.
An organizer of protest movement Tahrir Berlin told The Local, “through this visit Germany is enabling police-state terrorism.”
“Since Sisi has come to power 40,000 people have been imprisoned for political reasons. During this time 80 people have died in custody. It is now illegal to protests by law. Civilians are tried in military courts. This is fascism,” she said at a small protest outside the Egyptian embassy in Berlin.
Another protester who identified himself as Nizar said “I don't feel safe going back to Egypt. This shows the German government doesn't care about my fate.
“Its all about business, they don't care about democracy,” he said. “But if you pressure Egypt you will get change.”
The visit also drew criticism in the German media over Cairo's support of repressive Arab regimes in the fight against Islamist extremism.
Sisi, Egypt's former army chief, ousted Islamist president Mohamed Morsi in July 2013 and launched a deadly crackdown against his Muslim Brotherhood supporters as well as secular activists.
The crackdown has left hundreds of Morsi supporters dead and thousands jailed, while dozens have been sentenced to death in mass and speedy trials, including Morsi himself who is awaiting a final ruling on his sentence.
Merkel said Germany always opposes capital punishment and that "under no circumstances, even with regard to terrorist activities, must people be sentenced to death", while also stressing the need for continued bilateral dialogue.
At the joint press conference, a woman shouted at Sisi and called him a "murderer", leading many Egyptian journalists to defend the president and shout "long live Egypt", as both Sisi and Merkel were led out of the noisy room by security guards.
German parliament speaker Norbert Lammert had earlier called off a meeting with Sisi citing the "systematic persecution of opposition groups with mass arrests, convictions to lengthy prison terms and an incredible number of death sentences".
Sisi during his two-day visit however did meet President Joachim Gauck, and was also due to hold talks with Vice Chancellor Sigmar Gabriel and Foreign Minister Frank-Walter Steinmeier.
Egyptian media said he was expected to sign several agreements in the renewable energy and oil sectors during a meeting with top German companies.
Five prominent rights groups, including Amnesty International and Human Rights Watch, on Monday urged Merkel to press Sisi to end "the gravest human rights crisis in Egypt in decades".
Jörg Luyken contributed reporting.