Russia's Defense Ministry said the Israeli warning came less than a minute before the strike, and it accused the Israeli military of using the Russian plane as a cover to dodge Syrian defense systems.
Syrian air defences shot down the Russian military plane on Monday, killing all 15 soldiers aboard, after Israeli missiles had struck the coastal region of Latakia.
The incident marked the first mistake strike between Syria and Russian Federation, which is the main ally to the Syrian government.
However following anger among Russia's military brass and threats of "retaliation", Putin "reminded" Netanyahu that such operations "violated Syrian sovereignty" and said "agreements around the prevention of unsafe incidents were not observed", according to the Kremlin.
Israel said it had targeted a Syrian military facility where weapons manufacturing systems were "about to be transferred on behalf of Iran" to Lebanese Shiite group Hezbollah.
The military said the plane disappeared as four Israeli fighter jets were attacking targets in the area. It added that Israeli planes were already in Israeli airspace when Syria fired the missiles that hit the Russian plane.
Syria's SANA news agency reported on Wednesday that Assad had sent a telegram to Moscow saying he was sorry about the death of Russian military service people, but blamed Israel for the downing.
Qatar praises Turkey-Russia deal to 'demilitarize' Idlib
Throughout the fighting, Israeli Prime Minister Benjamin Netanyahu has maintained continuous contact with Russian Federation . The Russian Ministry said the meeting was to do with the loss of the Russian plane.
Israel on September 18 said Syrian antiaircraft batteries "fired indiscriminately" and failed to ensure that no Russian planes were in the air during the incident on September 17.
Prime Minister Benjamin Netanyahu told Russia's President Vladimir Putin by phone on Tuesday his forces would keep acting against Iran's military expansion in Syria.
Putin said he had signed off on the defence ministry statement.
It was the worst "friendly fire" incident between Moscow and the Syrian regime since Russian forces intervened in the country in late 2015 to support Assad whose grip on power had been weakened by rebels and jihadist fighters.
Lebanon's Hezbollah guerrillas, who like their patron Iran have been helping Assad militarily in Syria, said Israeli strikes there would not prevent them getting advanced weaponry.
Monday's attack came just hours after Russian Federation and Turkey negotiated a partial demilitarization of the Idlib province, which is the last remaining stronghold of anti-government militants, including the Al-Qaeda affiliate Hayat Tahrir al-Sham (also known as the Jabhat Al-Nusra).