In　this　paper　we　propose　two　theoretical　schemes　for　implementation　of　quantum　phase　gates　by　engineering　the　phase-sensitive　dark　state　of　two　atoms　subjected　to　Rydberg-Rydberg　interaction.　Combining　the　conventional　adiabatic　techniques　and　currently　developed　approaches　of　phase　control,　a　feasible　proposal　for　implementation　of　a　geometric　phase　gate　is　presented,　where　the　conditional　phase　shift　(Berry　phase)　is　achieved　by　adiabatically　and　cyclically　changing　the　parameters　of　the　driving　fields.　Here　we　find　that　the　geometric　phase　acquired　is　related　to　the　way　how　the　relative　phase　is　modulated.　In　the　second　scheme,　the　system　Hamiltonian　is　adiabatically　changed　in　a　noncyclic　manner,　so　that　the　acquired　conditional　phase　is　not　a　Berry　phase.　A　detailed　analysis　of　the　experimental　feasibility　and　the　effect　of　decoherence　is　also　given.　The　proposed　schemes　provide　new　perspectives　for　adiabatic　manipulation　of　interacting　Rydberg　systems　with　tailored　phase　modulation.　©　2017　American　Physical　Society.