Rumsfeld's visit to Tunis on Saturday was the first stop in a North African tour that will take him to Algeria and Morocco as well as Tunisia, all authoritarian Arab states that have been important US allies in the "war on terrorism".
The US and Tunisia are discussing a "status of forces agreement" that would enable an expansion of US-Tunisian military exercises and other activities, Rumsfeld said.
"We discussed the basis of the relationship," Rumsfeld said after talks with Zine El Abidine Ben Ali, the Algerian president, and other senior Tunisian officials.
Status of forces agreement typically establishes the rules governing US military presence in a host country by setting forth the legal rights and responsibilities of US military personnel.
Those discussions are "moving along", Rumsfeld said. "That would create a situation where we would be able to do more things, exercises and that type of thing."
The US currently provides Tunisia with $10.5 million a year in foreign military financing and another $1.9 million for training and education.
Rumsfeld also alluded to President George Bush's campaign to promote democracy in the Arab world both in comments to reporters and a statement he made following a meeting with Kamel Morjane, the defence minister .
US gives Tunisia $10.5 million a
year in foreign military aid
With Morjane at his side, he praised Tunisia's social and economic progress, but added that "political and economic freedom go hand in hand and each depends on the other for longterm stability".
For his part, Morjane read a brief statement affirming Tunisia's determination to strengthen friendship and cooperation with the US.
No questions were allowed, but it was the first time Morjane had ever appeared before the press, which is under tight government controls.
Demands for freedom of the press here gained international attention in November when government security forces reportedly harassed reporters covering a UN World Summit on Information Society, and denied entry to the head of Reporters Without Borders.
A senior US defence official said that while the US was encouraging Ben Ali to "think more creatively about political reform," it is "delicate".
"They do have a radical element that they do have to deal with," the official said.
Tunisia was the scene in April 2003 of a bombing outside what is reputed to be the oldest active Jewish synagogue in the world at Djerba.
"They have been attacked in this region," Rumsfeld told reporters. "They have felt the sting of that type of violence."
"They have had policies historically against violence and against terrorism, and have been I would say quite successful in doing the kinds of things with their population so that a peaceful and constructive approach is the normal here, as opposed to violence."
Rumsfeld, who arrived in Tunis from a Nato defence ministers meeting in Taormina, Sicily, was expected to sound similar themes in the visits to Algeria and Morocco.
On the flight here, he praised the three countries as "constructive partners" in the war on terrorism.
Ben Ali has been a staunch ally
in the US-led 'war on terrorism'
"We are continuing to participate with these three countries one way or another on military-to-military relations and that is something we value and want to strengthen," he said.
Also on Saturday, Aljazeera quoted Mauritania's prime minister Sidi Mohammed Ould Boubacar as denying press reports that a high-level US delegation currently visiting the country discussed with Mauritanian officials US plans to establish a military base in eastern Mauritania.
Aljazeera had earlier reported about the purported discussion.