As the first Lyceum produced show of David Greig's first season as artistic director – and a collaboration with director Ramin Gray and composer John Browne who staged Greig's successful The Events – The Suppliant Women marks an important moment for the Edinburgh theatre's development. Taking one of the earliest Attic tragedies and faithfully adapting it, Greig's script simultaneously emphasises both the shared concerns of fifth century Athens and contemporary Scotland and the cultural 'otherness' of ancient Greece. Issues of migration, racial identity and governance shape the narrative: the arrival of a group of refugee women in Argos provokes the city-state's king to consider the obligations of hospitality and trigger a referendum to resolve a moral quandary.

The production's twin aims – to recall the ritual nature of tragedy and recognise its continued relevance – ensure that the philosophical debate does not provide easy answers. While the script emphasises the righteousness of protecting the women – ratified by the democratic process – the attitude of the king towards immigrants, and their insistence on maintaining a cultural identity within their unfamiliar circumstances, makes a simple mapping of The Suppliant Women onto modern discussions difficult. Yet Gray's stripped back production, with the characters in modern dress and eschewing the machinery of setting and scenography for a simple public square, allows the arguments in Aeschylus' script plenty of space.

Equally, Browne's compositions provide the chorus with a series of dynamic odes, that engage musically and develop the themes. While the state's decision to protect the women is given democratic and religious sanction, Greig's adaptation of Aeschylus does not ignore the source's ambivalence about foreigners and the women's father's fragrant description of their daughters' blossoming sexuality – and insistence on their chastity – is disturbingly patriarchal, even creepy.

The decision not to exclude differences is bold, and, despite a final, celebratory ode of female empowerment, presents the issues not as a liberal plea for tolerance but as a complicated debate between holy law and political expediency. Greig's representation of Greek culture is sufficiently alienating to encourage further discussion, rather than reducing the matter to a rhetorical exercise.

The use of local women for the chorus of suppliants is powerful – echoing the Greek practice of enlisting citizens to perform – and their singing is beautiful even as they struggle with the choreography. The decision to use modern dress is distracting, especially in Oscar Batterham's King: suited like a MSP or businessman, he fails to achieve the gravitas of his position. While the costumes are intended to close the gap between the past and the future, they work against the production's recognition of tragedy's ritualistic roots. Reducing a King to a politician, Batterham lacks charisma and authority, making his pleas for tolerance more like the rehearsed and slippery karaoke of a time-serving official than an absolute monarch.

While Omar Ebrahim excels as Danaus, the father of the suppliants, his turn as an Egyptian herald is overwrought and camp in places, leaving his argument with the King disappointingly insipid. Since this concludes with a promise of war, this scene is stripped of its threat: the herald and his gang of thugs appear incapable of supporting their threats. At the heart of Aeschylus' narrative is the consequence of Argos' decision to protect the women – that the entire city will be massacred. The message, that doing the right thing even in the face of destruction, is obscured by this weak conflict.

Nevertheless, partially due to Browne's superb arrangements for voice, percussion and the ancient aulos, as used in the fifth century, The Suppliant Women is an intelligent attempt to reimagine Greek tragedy. While 'Brechtian' is often applied to any production that uses the relationship between audience and performers, Gray's vision of The Suppliant Women does evoke Brecht's sense of alienation, encouraging an active audience engagement with the ideas – not least through the articulation of attitudes that refuse to resolve into either liberal tolerance or conservative anxiety. From its preface, in which Omar Ebrahim enumerates the finances of the production, through the evocation of Aeschylus' focussed moral sophistication, to the finale's celebration of justice, The Suppliant Women is a dynamic exploration of theatre's potential as a space for political discussion, despite the flaws in some performances and occasional awkward juxtapositions due to the competing desires of relevance and reverence.

The Suppliant Women, Royal Lyceum, until 15 Oct, then touring.