"We've decided on an ambitious road map," Sarkozy told Algerian newspapers, referring to proposals on trade, investment, energy, and security with the gas-exporting nation.
He was ready to go "further" to build military co-operation and was "very open" to more arms sales to Algeria, he said.
Algeria is a former French colony while Tunisia, like France's closest Maghreb ally Morocco, was once a protectorate.
Sarkozy had been due to go on to Morocco but officials in Rabat, the capital, postponed it due to "scheduling problems".
The Moroccan move surprised many in the region, and some diplomats said the real reason was Rabat was annoyed Sarkozy was starting his tour in regional rival Algeria.
There has been no official comment from Rabat.
Morocco's leaders are close to Jacques Chirac, Sarkozy's predecessor, and enjoyed Chirac's support on the Western Sahara dispute, the main bone of contention in Moroccan-Algerian ties.
Sarkozy wants a new style in France's Africa policy, which he has said under Chirac was a cosy network of personal ties.
In an interview with Algeria's El Watan and El Khabar newspapers, Sarkozy defended France's longstanding refusal to apologise for colonial misdeeds in Algeria, saying leaders should focus on the future and not "beat their breasts".
Algeria, France's touchiest former overseas possession, has long demanded France apologise for killings during 132 years of colonial rule which ended with independence in 1962.
Sarkozy said: "Young people on either side of the Mediterranean are looking to the future more than the past and what they want are concrete things."
"They're not waiting for their leaders to simply drop everything and start mortifying themselves, or to beat their breasts, over the mistakes of the past because, in that case, there'd be lots to do on both sides."
Sarkozy's aides say he will explain his, as yet, vague plan for a Mediterranean Union, a formal partnership involving southern European countries and their North African neighbours.
Sarkozy also said French energy firms should have closer ties to Algerian oil and gas giant Sonatrach.
"We need to secure our gas supplies for the future, while Algeria can count on guaranteed and certain access to the French market and beyond to the European market," he said.