The Pentagon chief met with Azerbaijan's recently-elected President Ilham Aliyev and Defense Minister Safar Abbiyev.
"We do value the strategic relationship between our two countries," Rumsfeld told reporters in between meetings.
"We want our relations to cooperate in all these fields -- the economy, military, energy," Aliyev said.
There was speculation that Rumsfeld could use Azerbaijan, an oil-rich state wedged between Russia and Iran, as a jumping-off point for visits to other states in the region, but this has not been confirmed by Pentagon officials.
It was expected that Rumsfeld's talks in Azerbaijan would focus on growing military cooperation between the two countries, which are bound by a shared interest in the region's oil reserves and wariness of the intentions of Russia and Iran.
Analysts said the Pentagon could be seeking agreement on stationing US troops on Azeri soil as part of a Defense Department review of how American forces are deployed in Europe, Africa and the Middle East. Azeri officials have refused to confirm if this subject will be on the agenda for the talks.
General Chuck Wald, deputy chief of the US European Command, hinted earlier this year that troops could be deployed to Azerbaijan to protect the country's Caspian Sea oil fields and the pipelines for shipping the crude to western markets.
"Azerbaijan's territory is situated in the best place for US bases and provides the best flying times to the Middle East, Russia and even China," said Vafa Guluzade, a former state adviser on foreign affairs to the Azeri leadership.
Azerbaijan itself has much to gain from US military assistance, according to analysts.
It lies in a tough neighbourhood. To the north is Russia, its former imperial master which is competing with Washington for influence in the Caucasus region and control of the Caspian Sea's oil.
In the south is Iran, a country with which Azerbaijan has cool relations and which US President George W. Bush has designated as part of an "axis of evil."
In mid-2001, Tehran sent a gunship to press its claim to a prospective oil field in the Caspian Sea which Azerbaijan insists belongs to it. The two sides are now locked in a tense stand-off.
Some Azeri officials also suspect Iran of trying to export its Islamic revolution into Muslim but secular Azerbaijan.
The US defense secretary last visited Azerbaijan almost exactly two years ago, in the wake of the September 11 terrorist attacks in New York and Washington.
Since then the two countries have built close military ties. Azerbaijan is the only majority Muslim nation to send troops to Iraq, where it has a contingent of about 150 soldiers assisting the US-led security operation. Washington counts Baku as a member of its global coalition against terror.
The United States has returned the favour by providing several million dollars in military aid.
It is helping improve Azerbaijan's border security, it provides intelligence assistance and has contributed five second-hand coastguard cutters to bolster Azerbaijan's tiny Caspian Sea flotilla.
It was rumoured that the neighbouring Caucasus state of Georgia could also be on Rumsfeld's itinerary, though neither the Pentagon nor Georgian officials have announced that Rumsfeld will be going there.
Like Azerbaijan, Georgia has strategic importance for the West. It lies on the route of a pipeline being built by western oil majors which, when completed in 2005, will ship Caspian Sea oil to world markets.
Georgia's President Eduard Shevardnadze was deposed last month in a bloodless coup after protests sparked by rigged parliamentary elections.
He was replaced by an interim government which is keen to win the West's endorsement. But Russia is an influential player in Georgia and does not want to give Washington a free hand there, say analysts.