In a statement issued on the eve of the 99th anniversary of the deaths, Mr Erdogan unexpectedly described the events of 1915 as "inhumane", using more conciliatory language than has often been the case for Turkish leaders.
A Turkish Government official said it was the first time a Turkish prime minister had offered such explicit condolences, but it was not immediately clear if it would be enough to bring about a thaw in relations between Ankara and its neighbour.
The exact nature and scale of what happened during fighting that started in 1915 is highly contentious and continues to sour relations between Turkey and Armenia, a former Soviet republic. Turkey accepts that many Armenians died in clashes, but denies up to 1.5 million were killed and that this constituted genocide.
Mr Erdogan's statement - unusually released in nine different languages including Armenian - repeated previous calls for dialogue between the two countries, and the setting up of a historical commission to probe events surrounding the killings.
"It is with this hope and belief that we wish that the Armenians who lost their lives in the context of the early 20th century rest in peace, and we convey our condolences to their grandchildren," he said.
"Having experienced events which had inhumane consequences - such as relocation - during the First World War, should not prevent Turks and Armenians from establishing compassion and mutually humane attitudes among towards one another."