The base is a key element of the United States' security efforts in Afghanistan.
Rice is expected to hold talks with President Kurmanbek Bakiev and with Prime Minister Feliks Kulov later in the day.
Addressing reporters at the Kyrgyz National Opera and Ballet Theater in Bishkek, Rice said she had come to reiterate her country's support to the new political leadership that succeeded ousted president Askar Akaev last March.
"I came here to Kyrgyzstan so that you might know, whether in government or in civil society, that you will have a steady friend in the United States who believes too in democratic values, and as those democratic values take root in Kyrgyzstan, relations between the United States and Kyrgyzstan will also grow," Rice said.
Speaking to journalists on the plane that brought her to Bishkek, Rice earlier insisted that her trip to Central Asia should not be seen as directed against Russia, the other key player in the region.
Rice said the United States is aware that former Soviet republics in the area have been maintaining privileged ties with Moscow since 1991 and that it does not oppose these relations.
Rice's comments echoed remarks made on 6 October in Washington by State Department spokesman Sean McCormack.
Asked to comment on a summit of the Central Asian Cooperation Organization in the Russian city of St. Petersburg, McCormack denied that Washington and Moscow are vying for influence in the region.
"There is no [struggle for influence]. Our goals in this region are to build new kinds of relationships with the countries of this region. They are -- many of them -- developing democracies," McCormack said. "Many of them have started economic reforms where they are opening up to the rest of the world. We think it is an important region and Secretary Rice very much looks forward to going there and to talking with leaders in each of those countries about change in that region and about their individual relationships with the United States and how they might be different."
Christopher Langton of the London-based International Institute for Strategic Studies (IISS) told RFE/RL's Uzbek Service that he believes Rice's Central Asian tour carries no potential threat to Russia.
"It must be seen, partly, as a routine visit by a secretary of state. It's not the first time that a secretary of state, or other western secretaries of state, has visited Central Asia," Langton said. "I wouldn't make too much of that. But at the same time, Rice's agenda will be to establish more firmly U.S. interests in the region. Some analysts would suggest that that might be against Russian and Chinese interests, but I think it's going too far to suggest any kind of a re-igniting of outright competition in this area. I think Russia sees some advantages in some areas of having U.S. interests in the region, particularly vis-a-vis helping with democracy and also with economic development."
Besides Kyrgyzstan, the U.S. has access to military facilities in Tajikistan -- where Russia also maintains troops.
The United States has also been leasing a military base in neighboring Uzbekistan. But relations between Tashkent and Washington have soured following last May's bloody crackdown in Andijon and the Uzbek government has given American troops a few months to vacate the Karshi-Khanabad base.
Langton said he expects Rice to sound out Kyrgyz and Tajik leaders on ways to maintain the existing military cooperation with the United States.
"I think we need to look at Kyrgyzstan and Tajikistan, possibly, in one bracket, as countries [that] assisted the U.S. with the allocation of air-base facilities [on their territory] for operations in Afghanistan," Langton said. "And I think the secretary of state will want to pass the message firstly, obviously, that [the Americans] are very grateful for this and, secondly, that they would like to negotiate continuity of that arrangement for the foreseeable future."
Russia earlier this month announced plans to invest several billions of rubles to upgrade its air base in Kyrgyzstan. Also, unconfirmed reports from Tajikistan last week suggested Moscow is considering setting up a new air base in Tajikistan.
But whether these plans will be implemented remains under question.
Russian independent Central Asia expert Vitalii Portnikov said that -- pending action from Moscow -- regional countries have an interest in strengthening military ties with the United States.
"It seems to me that the most important part of [Rice's] visit to Central Asia is whether the ongoing cooperation between the U.S. and some of these Central Asian countries will be maintained," Portnikov said. "Whatever Russia's declarations regarding its cooperation with Central Asian countries, it remains unable to provide any real assistance to [the region] with regard to the fight against terror or drugs smuggling."
If security issues are expected to dominate Rice's visit to Kyrgyzstan and Tajikistan, experts believe she will shift her focus when she meets Kazakh President Nursultan Nazarbaev later this week.
"In Kazakhstan, I think, [the purpose of Rice's visit] is slightly different, it has more to do with the coalescing of interests between Russia, China, the U.S., and perhaps Europe in the energy resources," Langton said. "There is already a developing competition in Central Asia over that particular issue. The U.S. will [also] want to reiterate [its] support to reforms in Kazakhstan, possibly democratization, which is beginning to take root with the presidential elections coming up in December. Those are the main issues."
Speaking to reporters ahead of her arrival in Bishkek, Rice urged regional leaders to hold free and fair elections, saying the U.S. will regard any progress toward democracy as one of the key elements of its relations with Central Asian states.
Although she did not refer specifically to any particular country, the United States has recently expressed its concerns at steps taken by the Kazakh government against independent media in the run-up to the December polls.
Also last week, Washington expressed concerns over the sentencing of Tajik opposition leader Makhmadruzi Iskandarov, who received a 23-year jail term on terror-related charges.
Tajikistan is set to hold presidential polls next year. If reelected, President Emomali Rakhmonov will remain in power for another seven years.
(RFE/RL's Kyrgyz Service and Uzbek Service correspondent Shanat Sharipov contributed to this report)
Secretary Of State Rice Prepares To Visit Central Asia, Afghanistan
Central Asia: Q&A With U.S. Assistant Secretary Of State Daniel Fried
For RFE/RL's full coverage of events in Central Asia, see "Central Asia In Focus"