* Ukraine tightens controls on "men of an active age"
* Moscow demands clarification, says may retaliate
* Russian airlines issue warning to passengers
* Two countries share close business, family ties (Adds Russian response)
KIEV/MOSCOW, April 17 (Reuters) - Ukraine said on Thursday it will impose stricter border controls on Russian men trying to enter the country, where separatist rebellions have broken out, prompting Moscow to threaten retaliation.
The Kiev government, which has accused Moscow of stirring up trouble in the largely Russian-speaking east, said it would target checks on "men of an active age" due to "possible provocations".
However, any restrictions on movements between the neighbouring states - which share close cross-border family and business ties - risk aggravating a crisis which erupted when pro-Moscow Ukrainian President Viktor Yanukovich was ousted in February and Russian troops seized control in Crimea.
Russian airline S7 said three passengers on flights from Moscow to the Ukrainian city of Odessa had been turned back, the Interfax news agency reported.
Kiev tightened the controls as foreign ministers from Ukraine, Russia and the United States held talks in Geneva along with the European Union's foreign policy chief on calming the crisis.
"From today the Ukrainian border control service has significantly increased checks at the border with Russia," a spokesman for the service, Oleh Slobodian, said.
"This applies to Russian citizens because there is information about possible provocations at the border, up to and including terrorist attacks. Attention will be primarily paid to men of an active age, traveling alone or in a group."
The announcement drew a sharp response from Moscow, which has denied interfering in eastern Ukraine and accuses Kiev of causing the crisis by ignoring the rights of Russian speakers.
"Russia insists on an immediate official clarification from Ukraine on steps taken by the Ukrainian state border control service. Upon receiving the relevant information from Kiev, we will consider appropriate retaliatory measures," the Foreign Ministry said in a statement.
Russia's flag carrier Aeroflot earlier issued a statement warning passengers that the Ukrainian authorities were "massively restricting" entry to the country.
It indicated that men between the ages of 16 and 60 would be denied entry unless they had proof of a reason to visit, such as family ties or an invitation from a business or individual, or were travelling with their families.
Most Ukrainian passport holders who are residents of Crimea - which Russia annexed last month - will also face stricter border checks, the airline said.
(Reporting by Pavel Polityuk in Kiev and Alissa de Carbonnel in Moscow; Editing by Steve Gutterman and David Stamp)