Russian President Vladimir Putin (R) meets with Israeli Prime Minister Benjamin Netanyahu at the Novo-Ogaryovo state residence outside Moscow, Russia, ion this file photo dated September 21, 2015. REUTERS/Mikhail Klimentyev/RIA Novosti/Pool

JERUSALEM (Reuters) - Russian forces in Syria have fired at least twice on Israeli military aircraft, prompting Prime Minister Benjamin Netanyahu to seek improved operational coordination with Moscow, Israel's top-selling newspaper said on Friday.

Asked about the alleged incidents, however, Kremlin spokesman Dmitry Peskov said: "In this case, Israeli press reports are far from reality."

But Netanyahu, in remarks published by Israeli reporters whom he briefed by phone on his talks on Thursday with Russian President Vladimir Putin, said "there have been problems" regarding Israeli military freedom of operation in Syria.

He gave no details, but said: "If you don't deal with the friction, it could develop into something more serious."

The unsourced report in Yedioth Ahronoth made no mention of dates or locations for the two reported incidents, nor did it give any indication of whether the Israeli planes were hit.

Russia mounted its military intervention in Syria in September to shore Damascus up amid a now 5-year-old rebellion.

Separately, Israel's Channel 10 TV said a Russian warplane approached an Israeli warplane off the Mediterranean coast of Syria last week but that there was no contact between them.

An Israeli military spokesman declined comment. Netanyahu's office and the Russian embassy in Israel did not immediately respond.

Israel, which says it has carried out dozens of bombings in Syria to foil suspected arms handovers to Lebanese Hezbollah guerrillas, was quick to set up an operational hotline with Moscow designed to avoid accidentally trading fire with Russian interventionary forces.

In Moscow on Thursday, Netanyahu told Putin in televised remarks: "I came here with one main goal - to strengthen the security coordination between us so as to avoid mishaps, misunderstandings and unnecessary confrontations."

In an apparent allusion to Syria, Putin said: "I think there are understandable reasons for these intensive contacts (with Israel), given the complicated situation in the region."

According to Yedioth, the reported Russian fire on Israeli planes was first raised with Putin by Israeli President Reuven Rivlin, who visited Moscow on March 15. At the time, Putin responded that he was unaware of the incidents, Yedioth said.

(Writing by Dan Williams and Jeffrey Heller; Additional reporting by Maria Tsvetkova in Moscow; Editing by Hugh Lawson)