They also include some of the areas where Turkey, a North Atlantic Treaty Organisation ally, has skirmished with Kurdish militias that are backed, sometimes with airstrikes, by the United States.
The Britain-based Observatory said a child was killed in government shelling in parts of Homs province that fall within the de-escalation zones, the first civilian death in the zones since the deal began coming into effect.
"The case is that in the de-escalation zones, the work of aviation, especially the coalition forces, is absolutely not envisaged, with or without notification", Alexander Lavrentyev, the head of Russia's delegation in peace talks and Russian President Vladimir Putin's special envoy for Syria said.
He said they would be allowed to fly only in eastern Syria over areas held by the Islamic State extremist group, apparently excluding the entire western spine of the country.
The conflict occurred in the rebel-held village of al-Zalakiyat as fighter jets fired in the Hama countryside, reported the Syrian Observatory for Human Rights.
The group also said the deal was an attempt to neutralize rebel-held areas and give Syrian government troops the military victories they could not achieve on the battleground. There was no immediate comment from the Syrian army.
Mohammed Rasheed, a spokesman for the Jaish al-Nasr rebel group based in Hama, confirmed that fighting had broken out after midnight.
Rasheed said rebel-held Idlib province to the north of Hama was nearly completely quiet, but the attacks, which included barrel bombs, were focused on the northern Hama frontline area.
Vasquez said the Russians' interpretation of their own agreement "makes no sense".
Iran and Turkey agreed on Thursday to Russia's proposal to establish the de-escalation zones.
The call came as a Russia-initiated plan to set up safe zones was to take effect. Weaponry and air strikes were not to be used in those zones by combatants, the text said.
The Astana talks were meant to shore up an oft-violated ceasefire originally agreed in December.
Tensions between the USA and Russian Federation have worsened in the weeks since the US missile strike.
US Secretary of State Rex Tillerson discussed Syria with Russian Foreign Minister Sergei Lavrov on Friday, and General Joseph Dunford, chairman of the US Joint Chiefs of Staff, spoke with his Russian counterpart General Valery Gerasimov on May 6.
The zones appear meant to halt conflict in specific areas between Assad regime forces and opposition fighters, and would potentially be policed by foreign troops.
However, the United States is not part of the deal, and the Syrian armed opposition refused to sign it, saying that Iran, which it considers a party in the conflict, should not be a guarantor. "And it is not a coincidence that the United States has welcomed the result of the Astana meeting - an agreement to create de-escalation zones", Lavrov said.