Muslims want the American Federal Bureau of Investigations kicked out of Kenya.
And they also want the Suppression of Terrorism Bill withdrawn because it could turn the country into a police state.
In a memorandum presented to President Kibaki, 58 Muslim leaders said FBI agents should leave because Kenyan security was capable of carrying out investigations.
But responding to the memorandum before he ended his two-week visit to the Coast on Monday, the President assured Muslims that the terror Bill would be refined before being sent to the House.
President Kibaki assured Muslims that sections that could lead to unnecessary harassment of Kenyans would be removed from the Bill after consultations.
The twin issues of the FBI and the anti-terror Bill were raised by the Mombasa branch of the Supreme Council of Kenya Muslims (Supkem) chairman, Sheikh Juma Ngao, when the leaders visited the President at State House, Mombasa.
Other issues included the constitutional review talks, the Kadhi's court, education, development, natural resources, health, employment, religious donors, agriculture and land.
The President asked Muslims to help the Government in its free primary education campaign to ensure more children at the Coast were enrolled in schools.
Those in the delegation were Mr Mohamed Kidzeru, Mr Amir Juma Fundi, Sheikh Badawy, Sheikh Amir Khamis Banda, Mr Khamisi Mwaguzo, Sheikh Salim Mwarangi and Sheikh Yusuf.
Others were Sheikh Ali Maawy, Sheikh Ali Darani, Sheikh Salim Sharmani, Sheikh Islam Saidi, Sheikh Abbas Dola, Mr Omar Shimasi, Sheikh Shee Juhudi and Sheikh Kassim Salim.
The leaders opposed the use of foreign detectives in the hunt for terrorists, saying the existing Kenyan laws were sufficient to enable police deal with any crime.
"We see it (Bill) as a direct insult to our religion and instrument of harassment. Presently, many Muslims are arrested then set free after they and their families have been harassed," they said.
In the memorandum, the leaders claimed Muslims were being discriminated against by the State when seeking funds from foreign donors, unlike Christians.
"The churches are allowed to receive donations from Europe and the United States while Muslims are stopped from receiving donations from other Muslim countries," they said.
They blamed this on pressure from the US, adding that such action was damaging Islam in Kenya and was forcing Islamic preachers and teachers to go without salaries. It was also forcing Islamic institutions to cut their expenditure or close down altogether.