Mr Abhisit made the statement Sunday before Democrat MPs are due to meet government ministers tomorrow to propose a set of measures to solve the southern violence.
He said Ms Yingluck should not delegate the tasks tackling southern unrest to too many people, as it could create confusion.
He said the prime minister still plays a central role in overseeing tasks which involve security operations and development projects. "Confusion will ensue if responsibilities are given to many people," he said.
Mr Abhisit said it was too early to conclude that the surrender of suspected militants was a government success.
He said many insurgent groups which do not turn themselves in could still pose potential problems.
Mr Abhisit said it is up to the government whether to make use of the information.
He said the party had submitted several proposals to solve the southern problem but the government did not heed them.
The Democrat Party has come up with nine proposals to be presented to the government tomorrow.
They include stopping deploying troops from other regions to the far South and using troops from the Fourth Army, which oversees security in the area. Another idea is the government should make sure victims of the unrest receive the same compensation as those affected by political unrest in Bangkok between 2005 and 2010.
The Democrats oppose a proposal by Deputy Prime Minister Chalerm Yubamrung to set up a special administrative system for Yala, Pattani, and Narathiwat in which the governors of the three southernmost provinces would be elected and have some degree of autonomy.
The Democrats said the Southern Border Provinces Administration Centre should be a key agency in administering justice while the Internal Security Operations Command takes charge of security operations.