Tensions between the two South Asian neighbours have been rising since the killing of two Indian soldiers by Pakistani troops along the LoC earlier this week.
"The need of the hour is to maintain the spirit of the ceasefire all along the Line of Control at any cost," the patron of Jammu and Kashmir People's Democratic Party said while addressing party workers here.
He added that peace on the border was in the interest of the people of the state because they "bear the brunt of the hostility between the two countries".
Mufti expressed concern over what he described as "unpleasant events on the LoC recently" and said concerted steps must be taken to avoid reoccurrence of such incidents in future.
He said the ceasefire announced on the border by the former prime minister Atal Bihari Vajpayee in 2003 brought positive changes in the lives of the common people in the state.
"For the people of Jammu and Kashmir, the ceasefire has brought peace in their lives. So, I am hopeful the leaderships of the two countries would realize the importance of maintaining the spirit of the ceasefire," he said.
The former chief minister said: "Leadership of India and Pakistan must act with political wisdom and not allow the hawkish rhetoric to spoil the gains of the peace process and the ceasefire."
The PDP patron also said that the ceasefire had laid the foundation for initiating the process of peace and reconciliation in the region along with historic initiatives like opening up of the LoC for bus service and trade.
Mufti appealed to the governments of India and Pakistan to adopt "realistic and purposeful policy to establish lasting and sustainable peace" in the region.
