The Sinn Féin President says the Irish and British government should not give in to what he says was a planned walkout yesterday by unionists from talks in the North.
The discussions on parades, flags and the past broke down in a row over a Parades Commission ruling.
The PSNI says it will uphold the ruling by the Parades Commission in relation to the July 12th parades.
The organisation has refused Orange Order bands permission to march past Ardoyne.
Both the DUP and UUP parties have pulled out of Stormont talks in protest at the ban.
The North's First Minister Peter Robinson branded the Parades Commission a 'shambles', saying recent decisions to restrict Orange marches have had a destabilising effect.
While the Deputy First Minister Martin McGuinness has said they now face a tense couple of weeks ahead.
Gerry Adams says this row should not threaten the peace process and institutions.
While the PSNI chief George Hamilton has also appealed for calm and says the police are prepared.