Fiji police are reported to have arrested about a dozen people protesting against the new constitution.
Fiji Women's Rights Movement says among those taken into custody are three of its members who were outside Government House as the president is about to assent to the new constitution.
It says the Criminal Investigation Department has seized their phones but no charges have been laid.
The leaders of the United Front For a Democratic Fiji have reportedly presented a letter to the President to express their opposition to the constitution.
Among its members are Mick Beddoes and Tupeni Baba of the Social Liberal Democratic Party, Mahendra Chaudhry of the Fiji Labour Party and Attar Singh of the National Federation Party.
Mr Beddoes has told FBC News that the letter calls on the President not to assent to the Constitution, but instead appoint a caretaker government that will take over until elections promised for next year.
The Attorney General, Aiyaz Sayed-Khaiyum, has earlier said there was good feedback from people and the international community on the document.
It has been strongly criticised by Amnesty International and Human Rights Watch.