In Israel, Mr Martin plans to meet Prime Minister Benjamin Netanyahu, President Isaac Herzog and Foreign Minister Eli Cohen.
He will also meet President Mahmoud Abbas in Palestine before travelling to Jordan, where engagements will include a meeting with Deputy Prime Minister and Foreign Minister Ayman Safadi.
“This visit is an important opportunity to see the political, security and human rights situation in Israel and the occupied Palestinian territory,” Mr Martin said.
“There has been a worrying escalation in violence over recent months.
“Ireland has been consistent in its calls for the protection of civilians and the application of international law.
“This visit will allow the opportunity to discuss directly these issues with political leaders, as well as with Ireland’s civil society partners.”
He added: “The visit will be my first to Jordan since the opening of Ireland’s embassy in Amman and I am looking forward to seeing the strengthened bilateral relationship between us, including Ireland’s support for the Jordan Young Scientist Programme and other innovation initiatives.
“Jordan also hosts a significant number of refugees from Syria, Palestine and elsewhere. I will meet with refugee families and UN partners and reiterate Ireland’s continuing support.”
Ireland does not recognise Palestine but is also critical of some of Israel’s policies.
The Tanaiste, as Ireland’s Deputy Prime Minister minister is called, will also meet UN leaders and other partners in the region.
Tensions have risen this year in the West Bank, resulting in the highest number of deaths recorded between Israelis and Palestinians since 2005, the UN said last month.
At least 225 Palestinians, 32 Israelis, a Ukrainian and an Italian have been killed in violence linked to the Palestinian-Israeli conflict, AFP reported.
Israel has conducted raids on refugee camps, towns and cities in the West Bank.
There have been major operations in Jenin and Nablus where dozens of people have been killed, including children, and hundreds wounded.