The European Union said late today its top diplomat Federica Mogherini was heading to Iran and Saudi Arabia for talks on Syria's five-year conflict.
Rebel groups including the Ahrar al-Sham faction and former Al-Qaeda affiliate Fateh al-Sham Front fired rockets into government-held western Aleppo, killing at least 15 civilians, a monitor said.
The rebels also targeted government positions east of Aleppo city and in the coastal province of Latakia, including the Hmeimim military base used by Russian forces allied with the regime.
But the Kremlin said Putin did not agree to the request.
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"The Russian president considers it inappropriate at the current moment to resume strikes on Aleppo," Kremlin spokesman Dmitry Peskov said, adding that Putin thought it necessary to "continue the humanitarian pause" in the war-ravaged city.
"The Russian side retains the right in case of extreme necessity to use all the troops and facilities it has to carry out support of the Syrian armed forces at the necessary level," he added.
Today's rebel assault comes more than three months into a government siege of eastern Aleppo, where more than 250,000 people live, and several weeks after the army began an operation to retake the rebel-held east.
Rebel groups "announce the start of the battle to break the siege of Aleppo", said Abu Yusef Muhajir, a military commander and spokesman for Ahrar al-Sham.
The assault "will end the regime occupation of western Aleppo and break the siege on the people trapped inside", he told AFP.
The Syrian Observatory for Human Rights, a Britain-based monitor, said at least 15 civilians, including a woman and two children, had been killed, and more than 100 wounded in rebel fire on western Aleppo.