Mr Cavusoglu’s visit comes as Turkey seeks to strengthen its international ties amid economic woes at home and before elections next year.
“We will continue our strong support for the Palestinian cause,” the Turkish official said after talks with his Palestinian counterpart Riyad Al Maliki.
Turkish President Recep Tayyip Erdogan has been a vocal critic of Israel’s treatment of Palestinians, but his government has sought to revive ties with Israel in recent months.
The Turkish foreign minister’s decision to meet Palestinian officials first stands in contrast to visits by most European and US delegations, which tend to prioritise talks with Israeli leaders.
During his visit to Ramallah in the occupied West Bank, Mr Cavusoglu pledged to boost trade with Palestinians. He is also due to meet Palestinian President Mahmoud Abbas.
Mr Cavusoglu will travel on Wednesday to Jerusalem, where he will hold talks with Israel’s foreign and tourism ministers.
He is also expected to make a visit without Israeli officials to Al Aqsa Mosque in occupied East Jerusalem.
Mr Erdogan last month slammed Israeli “interventions” against Muslim worshippers at the mosque compound, which is located in the heart of the Old City.
Israeli riot police fired rubber bullets and beat Palestinians with batons at Al Aqsa, the third holiest site in Islam.
Jordan serves as custodian to the mosque compound but access is controlled by Israel. The site is known as Temple Mount to Jews, who are allowed to enter the compound but not pray there.
Mr Cavusoglu’s visit to the Old City will follow talks with his Israeli counterpart Yair Lapid, the first such meeting in Jerusalem for several years.
Turkey recalled its diplomats from Israel in 2018 after Israeli forces killed dozens of Palestinians in protests along the Gaza border.
That move followed Ankara’s earlier decision to cut ties after Israeli forces stormed a ship in 2010 that was leading a flotilla to the blockaded Gaza Strip. Ten Turkish civilians were killed in the raid.
Bilateral ties thawed earlier this year, with a visit to Ankara by Israel’s president for the first time in 15 years.
Mr Erdogan said the decision to host Israeli President Isaac Herzog in March marked a “turning point” in relations.