BISHKEK, Kyrgyzstan — Kyrgyzstan's deposed president said Tuesday he will resign if the interim authorities guarantee his security, and the head of the security services said he was ready to make such a promise.The statements could point to a resolution of the tensions that have gripped the country since President Kurmanbek Bakiyev fled the capital during an uprising that left at least 83 people dead last week. The tensions in the impoverished, strategically important former Soviet Central Asian nation worry the United States and Russia, both of which have military bases in Kyrgyzstan.The US base, at the capital's international airport, is a key piece in the NATO military campaign against the Taliban in Afghanistan, providing refueling flights for warplanes over Afghanistan and is a transit point for troops.Bakiyev told a news conference in his home southern village of Teyit that "I will resign if security is guaranteed for me and my relatives."Shortly thereafter, the head of the security service of the interim government, Keneshbek Duishebayev, said "we are ready to guarantee security to him and his family."However, when asked specifically about Bakiyev's brother and son, Duishebayev declined to comment. Those men are among the Bakiyev relatives most often accused of reaping massive wealth through improper channels; complaints about corruption were a prime issue in the events that drove him out of the capital.Bakiyev did not detail what sort of security guarantees he was lookingfor. The opposition figures who formed a self-declared interimgovernment after he fled the capital had previously offered him safepassage out of the country, but Bakiyev has shown no intention ofleaving Kyrgyzstan and there are doubts about whether any country wouldaccept him.He also proposed that Roza Otunbayeva, the head of the interimgovernment, come to his southern home base for talks and guaranteedsafety for her and other officials.Bakiyev made his resignation offer hours after rallying with about5,000 adherents in an apparent test of how much support he could musterfor resisting the opposition authorities. Although the crowd ofsupporters that greeted Bakiyev on Tuesday was highly emotional, therehave been persistent doubts about how much backing he has and whetherhe commanded enough loyalty in the security forces to mount seriousresistance.In turn, Bakiyev appeared unwilling to push the stalemate into newviolence, warning his supporters that "the whole world is watching us."