Mr Lavrov, whose government a close ally of the Syrian regime, said some victims had been killed at close range in a district controlled by rebels.
The UN condemned the killings, saying government artillery was involved.
UN-Arab League envoy Kofi Annan has arrived in Damascus for talks on implementing his peace plan.
He called on “every individual with a gun” to lay down their arms.
“I have come to Syria at a critical moment in this crisis,” Mr Annan said shortly after his arrival.
“I am personally shocked and horrified by the tragic incident in Houla.”
At a joint news conference with UK counterpart William Hague in Moscow, Mr Lavrov said that Russia was “deeply alarmed” by the massacre in Houla.
“We are dealing with a situation in which both sides evidently had a hand in the deaths of innocent people,” he said.
“There is no doubt that the government used artillery and tanks and this has been reported by UN observers who have visited the scene.
“There is also no doubt that many bodies have been found with injuries from firearms received at point-blank range. So the blame must be determined objectively.”
He said the causes of the massacre must be understand so that it could never be repeated.
Asked if President Bashar al-Assad could be part of the solution in Syria, he said that ending the violence was more important than who was in power.
“We do not support the Syrian government. We support the plan of Kofi Annan,” he said.
The Syrian government insists the killings were carried out by “terrorists”.
Analysts earlier expressed surprise at Russia’s support for the UN Security Council condemnation of the Houla killings. Moscow has so far been reluctant to apportion any blame for deaths in Syria to the Assad regime.
Mr Hague renewed Britain’s call for Mr Assad to comply with Mr Annan’s peace plan.
“The alternatives are the Annan plan or ever increasing chaos and a descent closer and closer to all-out civil war and collapse,” he said.
Forty-nine children and 34 women were among Friday’s dead, the UN has confirmed.
On Monday, China also condemned the “cruel killings”.
The BBC’s Jim Muir in neighbouring Lebanon say there is no sign that the Syrian government’s behaviour on the ground has changed as a result of the Houla massacre.
Fighting in Syria has continued despite the deployment of some 280 UN observers monitoring the ceasefire brokered by Mr Annan.
Opposition activists said at least 30 people were killed on Sunday when the army shelled the central city of Hama. The reports cannot be independently verified.
On Sunday the Security Council unanimously adopted the non-binding statement calling for the Syrian government to withdraw its heavy weaponry from residential areas and return them to barracks.
The statement also condemned the Houla killings, saying they involved both government artillery and gunfire at close range.
Syria’s UN ambassador, Bashar Ja’afari, accused some members of the council of trying to mislead the world.
“Neither [UN observer mission head Maj Gen Robert] Mood nor anybody else told the Security Council in the informal session that he would blame the Syrian government forces for what happened,” he said.
Gen Mood told the BBC that UN monitors were continuing their investigations in Houla.
Mr Annan arrived in Damascus on Monday and will hold talks with President Assad on Tuesday.
Under Mr Annan’s plan, both sides were to stop fighting on 12 April ahead of the deployment of monitors, while the government was to withdraw tanks and forces from civilian areas.
The unrest in Syria has killed at least 10,000 people since protests against President Assad broke out in March 2011.