US President Joe Biden told Turkish President Tayyip Erdogan his request for F-16 fighter jets had to go through a process in the United States, while Erdogan said his counterpart was "positive" toward the jet sale.
Ties between Ankara and Washington have been strained over a host of issues in recent years, from policy differences in Syria to Turkey's purchase of Russian S-400 missile systems, human rights and legal matters. The United States has also sanctioned Turkey over the S-400s.
Days after the allies narrowly averted a diplomatic crisis over jailed philanthropist Osman Kavala, Biden and Erdogan met on the sidelines of the G20 summit in Rome. Biden also raised the issue of human rights, a US senior administration official told reporters.
"President Biden reaffirmed our defense partnership and Turkey's importance as a NATO Ally, but noted US concerns over Turkey's possession of the Russian S-400 missile system," the White House said in a statement after the meeting.
The Turkish presidency said the two leaders had agreed to form a joint mechanism to strengthen ties, while a senior Turkish official said the talks were held in "a very positive atmosphere".
Speaking to reporters in Rome, Erdogan said he reiterated to Biden Turkey's opposition to US support for the Syrian Kurdish YPG - a US ally in the fight against Islamic State in northeast Syria but deemed a terrorist group by Ankara.
"Undoubtedly, I conveyed to him (Biden) our sadness with the support these terrorist organisations in Syria... are receiving from the United States," Erdogan said. "I also told him these issues were steps that could damage our solidarity."
Ankara had previously ordered more than 100 F-35 jets, but Washington removed Turkey from the programme after it bought the S-400s. Turkey has called the move unjust and demanded reimbursement for its $1.4 billion payment.
Erdogan has said that payment should be used to finance some of Turkey's request to buy 40 F-16s and nearly 80 modernisation kits, but Washington has said it had made no financing offers to Ankara.
Erdogan said he asked Biden for support in getting US lawmakers to back the sale.
"While I saw Mr Biden's positive approach on this matter, another aspect of the issue is the House of Representatives and Senate," he said.
On Saturday, a different US administration official said that Biden would warn Erdogan against "precipitous" actions and that crises should be avoided after the Turkish leader last week threatened to expel 10 foreign envoys, including the US envoy, for seeking Kavala's release. Erdogan withdrew his threat on Monday.