The controversy between authorities and the activists is over the site of the planned protest on Friday, as the opposition-backed youths insist on holding the rally at a square in the heart of the capital Kuwait City.
Authorities are offering a seaside square opposite the parliament building, saying the location can be easily protected.
"Security authorities will not allow any demonstrations or processions outside this square [opposite parliament]," Kuwait's Interior Minister Sheikh Ahmad al-Humoud Al-Sabah warned in an interview with the official KUNA news agency on Wednesday.
The minister, however, said the government believes in the right of assembly for citizens and their right to freedom of expression.
Last Friday, several hundred activists staged a rally in the heart of Kuwait City and then moved to a site just outside the government seat to demand the removal of Prime Minister Sheikh Nasser Mohammad al-Ahmad Al-Sabah.
Activists are protesting against the prime minister for refusing to face questioning in parliament for allegedly squandering public funds and committing financial and administrative irregularities.
Pro-government MPs backed by cabinet ministers voted on 17 May to refer the quiz filed by opposition MPs to the constitutional court on suspicion of breaching the constitution.
The 71-year-old Sheikh Nasser, a nephew of the emir, has been targeted by the opposition since he was appointed premier in February 2006.
During this period, he resigned six times and formed his seventh cabinet just two weeks ago. Parliament was also dissolved three times and development plans have been stalled in this wealthy, oil-rich state.