Syria’s new interim leader, meeting on Tuesday with the president of Turkey, thanked him for backing the rebel forces that toppled the Assad dictatorship and said he now sought a deep strategic relationship that would benefit both their countries.

The meeting was President Recep Tayyip Erdogan’s first with Ahmed al-Shara, who led the offensive that toppled President Bashar al-Assad of Syria last month. Both countries have a lot riding on their relationship, and the public comments by the two leaders after they met in the Turkish capital, Ankara, made clear that they are both looking to the future.

Mr. al-Shara, who was appointed interim president by a group of rebel leaders during a closed-door meeting last week, thanked Mr. Erdogan and his people for their support for Syrian refugees and for the Syrian opposition during the war. He said that Syria sought a “deep, strategic relationship in all fields” that would benefit both countries.

This would include developing a “shared strategy to confront security threats in the region,” he said, specifically mentioning northeastern Syria, which is controlled by a Kurdish-led militia that is not under Mr. al-Shara’s authority.

Turkey considers that militia, which is backed by the United States to fight the jihadists of the Islamic State, a terrorist organization because of its ties to Kurdish militants in Turkey and Iraq who have battled the Turkish state.

Mr. Erdogan, too, spoke of unifying all of Syria under the new government and said he appreciated the new authorities’ “strong will to fight terror,” a reference to the Kurdish-led militia.

Turkey shares a long border with Syria, hosts more than three million Syrian refugees and had chilly relations with Mr. al-Assad for years. Mr. Erdogan began speaking of mending ties not long before Mr. al-Assad’s ouster.

Turkey worries that instability in Syria could lead more refugees to flee or prevent those already in Turkey from returning home. Turkey also has military posts in northwestern Syria and directly backs Syrian armed groups near the border.

For Mr. al-Shara, Turkey could provide critical support as he faces the monumental tasks of unifying Syria, reviving its battered economy and transforming a constellation of militias into a national army.

Turkey has been interacting with armed groups that Mr. al-Shara has led since early in the war because they controlled significant territory along Turkey’s southern border, and Turkish officials were among the first to visit him in Damascus after Mr. al-Assad’s fall.

Mr. al-Shara arrived in Ankara on a Turkish state jet and was welcomed on the runway by Turkey’s energy and natural resources minister, Alparslan Bayraktar.

Mr. Erdogan said that Turkey stood ready to help Syria rebuild its infrastructure and that it would work for the lifting of the broad sanctions imposed on the country to punish Mr. al-Assad. The sanctions could impede reconstruction efforts.

Mr. al-Shara concluded his remarks by inviting Mr. Erdogan to visit Syria and the two men warmly gripped hands.

Despite Turkey’s close ties with the new authorities in Damascus, it is struggling to fix its own economy after years of populist spending and persistently high inflation. It would be difficult for it to provide Syria with the financing it needs to restart the economy and begin rebuilding communities that were reduced to rubble during the war.

So Mr. al-Shara has also worked to build ties with the United States, European countries and Gulf Arab leaders.

Last week, Sheikh Tamim bin Hamad Al Thani, the emir of Qatar, became the first head of state to visit Mr. al-Shara in Damascus. And on Monday, Mr. al-Shara met in Saudi Arabia with Crown Prince Mohammed bin Salman, the kingdom’s de facto ruler. To what extent these leaders will help fund the new Syria remains to be seen.

Mr. al-Shara, a former member of Al Qaeda, announced a public break with the group years ago and now expresses more moderate Islamist views. The militia he leads remains classified as a terrorist organization by the United States and other countries.

Safak Timur contributed reporting.