The diplomat said he hopes Kyrgyzstan's presidential election will be what he called a "showcase" for the region.
"[I am here] to discuss with the president, the members of the government, the continued development of civil society here in Kyrgyzstan and our hopes for the democratic transition, peacefully, in a way that will be a showcase for the world, particularly this region," Armitage said.
Armitage said a democratic leadership transition in Kyrgyzstan would set an example for other Central Asian nations.
"The power of ideas which emanate from Kyrgyzstan, we believe, can change the region in the most positive way," Armitage said.
Akaev is officially serving his second term as Kyrgyz president and the constitution restricts a president from serving any more terms.
Akaev pledged last year not to seek a new term, becoming the first Central Asian leader to make such a promise.
But some in the Kyrgyz parliament have argued he could be eligible to stay for another term, and the constitutional court has been asked to rule on the issue.
Akaev today said he plans to stick to his promise not to seek a new term.
"We will conduct the election in full compliance with the constitution and have no intention of making any changes to it [constitution]," Akaev said.
Akaev and Armitage also discussed areas of cooperation, in particular U.S.-led operations in Afghanistan.
The United States has an air base with more than 1,000 troops in Kyrgyzstan to support combat operations in Afghanistan. U.S. troops are also deployed in Uzbekistan.
But Armitage said the U.S. does not intend to have permanent military bases in the region.
Akaev said the base in Kyrgyzstan is "an umbrella of security" for all of Central Asia. And he said that a secure Afghanistan is important for the whole region's stability.
"I'm guided by the following principle and express it at all international meetings. Support for Afghanistan, support for President [Hamid] Karzai and his government. By helping Afghanistan we help ourselves," Akaev said.
Armitage is now heading to Tajikistan.
(Agencies/RFE/RL's Kyrgyz Service)