HANGZHOU, China — President Obama sought on Sunday to heal a rift with Turkey, expressing his wholehearted support for its president, Recep Tayyip Erdogan, in the wake of the failed effort to oust him and promising America’s help in bringing the coup plotters to justice.

Obama’s comments, after he met with Erdogan before a Group of 20 summit meeting here, seemed calculated to smooth over hard feelings in Turkey, where some officials had blamed the United States for fomenting the July 15 uprising by elements of the military.

The president said nothing about Erdogan’s crackdown after the coup, in which tens of thousands of people were arrested.

And his reference to helping Turkey bring the perpetrators of the uprising to justice was not accidental: Erdogan is demanding that the United States extradite Fethullah Gulen, a Turkish Muslim cleric living in Pennsylvania whom he accused of inciting the coup.

“This is the first opportunity that I’ve had to meet face to face with President Erdogan since the terrible attempted coup,’’ Obama said, facing the Turkish leader across a long table. “We’re glad you’re here, safe, and that we are able to continue to work together.’’

The president papered over the fact that Turkey’s interests have diverged recently from those of the United States, particularly in Syria, where Turkish forces have intervened to prevent Syrian Kurds from making further gains in the northern part of the country.

The Kurds are trained and equipped by the United States, which views them as critical in the military campaign against the Islamic State. But Erdogan fears they are trying to create an unbroken Kurdish corridor just south of Turkey’s border with Syria.

Erdogan said it was important for the United States and Turkey to fight against all terrorist groups, not just the Islamic State. He checked off the acronyms of two Syrian Kurdish groups. “We have to embrace the same stance against all terrorist organizations around the world,’’ he said.