The Kremlin said Friday it "may consider" supplying Turkey with air defence systems in a further warming of ties after a feud over the downing of a Russian jet last year.

President Vladimir Putin and Turkish counterpart Recep Tayyip Erdogan held talks in Istanbul on Monday in which the prospect of supplying Ankara with air defence systems was brought up, Kremlin spokesman Dmitry Peskov told Russian news agencies.

"Various missile defence systems were mentioned and if the Turkish side so desires, Russia may consider the possibility of supplying Turkey in various ways," Peskov was quoted as saying.

Turkey's private NTV channel, citing Turkish foreign ministry sources, said earlier this week that Ankara was ready to accept an offer from Russia for a Turkish tender to build long-range air defence systems.

Turkish officials, contacted by AFP, said they had no information about any development.

Putin's visit to Turkey -- his first since the November 2015 downing of a Russian war plane by Ankara sparked the worst dispute between the countries since the Cold War -- saw each side pledge to step up cooperation in all areas including defence and technology.

The Kremlin strongman on Monday hinted that concrete measures would be taken to reinforce defence ties with Ankara.

"We are ready to continue this (military-technical) cooperation and boost it with serious projects of mutual interest," Putin said.

"Proposals from both sides are being studied, and I am certain they have all the grounds to be carried out."

Ankara last year cancelled a preliminary deal on air defence systems with China amid concerns from its NATO partners.

At the time, Turkish officials said Ankara had instead an ambitious plan to build a Turkish-made missile defence system.

Despite the warming ties, Moscow and Ankara remain far apart on the conflict in Syria, with Russia supporting leader Bashar al-Assad and Turkey wanting him out.