Initial priority should be given to much-needed relief measures, the Church said.
The Israel-Palestinian conflict in Gaza has claimed nearly 1,900 Palestinian lives, most of them civilians, and has left 67 Israelis dead, all but three of them soldiers.
A 72-hour ceasefire between Israel and Hamas began at 8am local time (0500 GMT) today.
The Scottish Catholic International Aid Fund (SCIAF) has announced it is sending £30,000 to provide emergency aid to thousands of people caught in the conflict.
SCIAF is working with sister charity Caritas Jerusalem and others to provide medical supplies to four hospitals, food, blankets, fuel, soap, buckets and trauma counselling to the most vulnerable.
The Right Reverend John Chalmers, Moderator of the Church of Scotland, said: "In the face of the particular tragedy of Gaza, and the disturbing loss of so many civilian lives, the Church of Scotland actively engages with its local contacts in the region and seeks to support and amplify their efforts in seeking a just and lasting peace for all the people.
"The Church joins with others in welcoming any genuine ceasefire in Gaza, by Israel or its opposing combatants, and we urge that it continues. Only an end to the Israeli military operation in Gaza and the firing of missiles into Israel from Gaza will lead to conditions from which a just resolution may come.
"However, this is only the first step towards tackling the humanitarian disaster for the people of Gaza. With others, especially the churches agency Christian Aid, we recognise without an end to the Israeli occupation of Gaza and the West Bank, which has been in place since 1967, there can be no full and lasting peace for either Palestine or Israel. The occupation must end."
The Church also called for sustained peace negotiations which should include all local parties and should seek a "secure country for Israelis" and a "viable homeland" for the Palestinian people.
It said the "scandal" of suffering in Gaza would only be alleviated through the full and committed engagement of the international community, especially the US, along with the other members of the Middle East Quartet (the UN, the EU and Russia) working with all the local and regional parties to start peace-building measures.
It said that it looks to the UK Government to play a full and committed part in this.
SCIAF director Alistair Dutton said: "The humanitarian situation in Gaza is horrific. As ever, ordinary people are bearing the brunt of the violence. More than 1,700 people have been killed, 8,000 wounded, and over 250,000 now homeless. Many civilians have been deeply traumatised by what has happened to them, including an estimated 125,000 children.
"SCIAF's partners on the ground are providing urgently needed food, clean water, medical supplies, counselling, hygiene kits including soap, toothbrushes and nappies, and other basic essentials such as blankets, cooking utensils and buckets.
"We are sending an initial £30,000 in emergency aid and will continue to work with our sister agencies in Caritas to get aid to those who need it most."