Mogherini's remarks came in a statement issued on Sunday after she met Kuwait's Emir Sheikh Sabah al-Ahmad Al Sabah and expressed EU support for his "relentless mediation efforts" in the dispute.
She called on "all the parties to enter into negotiations to agree clear principles and a roadmap for a swift resolution of the crisis".
The statement said the EU was ready to support the process of negotiations and assist in the implementation of a plan for the resolution of the crisis, in particular in the area of counterterrorism.
Sheikh Sabah has been mediating to resolve the crisis after Saudi Arabia, the United Arab Emirates, Bahrain and Egypt cut ties with Qatar, accusing it of supporting "extremist" groups. Doha strongly denied the allegation.
The quartet imposed a land, sea and air blockade on Qatar and issued a list of 13 demands.
The move has been condemned by various international rights groups, the United Nations and multiple governments. Qatar has rejected the demands.
On Friday, Qatar's Emir Sheikh Tamim bin Hamad Al Thani said in a televised address that his country was ready for dialogue to resolve the dispute, but stressed that any solution to the crisis must respect his country's sovereignty.
Source: News agencies