Following the meeting with Italy's premier, Nato's secretary general expressed cautious optimism about the prospects of a shaky truce holding between pro Russian rebels and Ukrainian forces.
"I welcome the recent indications of reduced fighting in Ukraine and we hope that the ceasefire now is finally going to be respected," he said. "It is important that all parties fully respect the ceasefire and withdraw heavy weapons.
"Russia has transferred in recent months over 1,000 pieces of equipment - tanks, artillery and advanced air defence systems.
"They have to withdraw this equipment and they have to stop supporting separatists." The Nato boss added: "It is important that all parties now respect the provisions of the Minsk agreement.
"And any attempt to expand further the territory held by separatists would be a clear violation of the Minsk agreement and the ceasefire.
"And it would be unacceptable to the international community."
Stoltenberg's comments came as Ukraine's military announced it was starting the withdrawal of heavy weapons from the frontline of the conflict.
The withdrawal of all weapons over a calibre of 100mm is meant to contribute to a buffer zone between the two warring sides of between 50 and 140 kilometres, depending on the range of the arms.
Under the terms of a peace plan signed by Kiev and the rebels this month, the withdrawal is meant to be completed in 14 days. The rebels insist they have begun to pull back their heavy weapons but OSCE monitors on the ground have so far been unable to verify the claims.