Tayyip Erdogan (left) and Joe Biden pose for a photo as they attend a bilateral meeting in Rome, Italy, on Sunday. Reuters

US President Joe Biden and his Turkish counterpart Recep Tayyip Erdogan pledged on Sunday to improve bilateral ties following a particularly tense period between Washington and Ankara.

Both presidents said that their countries must better manage disagreements after the partnership between NATO allies was tested by Turkey's threat to no longer recognise the American envoy and its purchase of a Russian missile defence system.

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“We’re planning to have a good conversation,” Biden said as the leaders appeared in front of journalists before nearly an hour of closed-door talks. The president did not answer questions about whether Turkey had grown too close to Russia or about human rights.

Recep Tayyip Erdogan (second from left) and US President Joe Biden (fourth from left) attend a meeting. AFP

Meeting on the sidelines of the G20 summit in Rome, the two leaders "had a very constructive conversation" in which Biden "made clear his desire to have constructive relations with Turkey and to find an effective way to manage our disagreements," a senior US administration official said.

In the meeting, Biden reaffirmed Turkey's importance as a NATO ally as well as its defence partnership with the US, but raised with Erdogan concerns about possession of the Russian S-400 missile system, the White House said in a statement afterward.

Turkey's 2019 purchase of a Russian S-400 air defence system has been an irritant on ties, prompting Washington to block Ankara's plans to buy about 100 next-generation US F-35 planes.

Erdogan has insisted on compensation, saying Washington could pay back at least part of the $1.4 billion advance payment Turkey made for the F-35s through the delivery of older-generation F-16 fighter jets.

Erdogan’s office said in a statement that the meeting was held in a "positive atmosphere” in which the leaders expressed a desire to "further strengthen and improve Turkey-US relations and agreed to establish a common mechanism accordingly.”