Gen Yuthasak said he wants peace in the country as a birthday present.
He said if it is possible, the two sides should hold talks to peacefully settle their conflict and end the ongoing political turbulence.
Asked about the possibility of another military coup, Gen Yuthasak said there is no factor justifying a coup at this time.
Whether or not there will be a coup depends on the situation, as the armed forces are duty-bound to maintain peace and protect the high institution, he added.
The minister said as he was assigned by caretaker Prime Minister Yingluck Shinawatra to oversee internal security on Jan 13, he would act as a coordinator between the armed forces and the Centre for the Administration of Peace and Order (Capo) for provision of military reinforcements to ensure law and order, if necessary.
Gen Yuthasak said he was invited to attend a function to mark the anniversary of the establishment of Army Region 1 on Jan 13, and he would take this opportunity to discuss the situation and ways to ensure people’s safety with army chief Prayuth Chan-ocha.
The People’s Democratic Reform Committee (PDRC), led by former Democrat MP Suthep Thaugsuban, plans to hold a mass Bangkok shutdown rally on Jan 13, to pressure Ms Yingluck and her caretaker cabinet members to step down.