Only the U.N. Security Council, on which Russia holds a controlling vote, can set and enforce such deadlines, he added.
"Ultimatums and artificial deadlines rarely help matters," Lavrov said. "Annan has a Security Council mandate and it is up to [it] to decide who is complying with this plan and how," he said.
The Friends of Syria group, an 80-country coalition including the United States, agreed to begin shipping money and supplies to the Syrian rebels.
However, neither the group nor the White House agreed to begin arming the rebels.
Congress remains divided on whether to arm anti-Assad forces in Syria.
Advocates of military support, such as Sens. John McCainJohn McCainWhy the GOP cannot sweep its Milo scandal under the rug New York Knicks owner gave 0K to pro-Trump group Hannity apologizes for sharing 'inaccurate' story about McCain MORE (R-Ariz.) and Joe Lieberman (I-Conn.), claim armed support is the only way to curb Assad's brutal crackdown on rebel forces.
But others on Capitol Hill are wary that such intervention might draw the United States deeper into another war in the Middle East, just as American troops are preparing to come home from Afghanistan.
Questions also remain on whether the United States and its allies can guarantee any weapons handed over to the Free Syrian Army won't end up in the hands of terror groups like al Qaeda.
Rep. Mike Rogers (R-Mich.), the chairman of the House Permanent Select Committee on Intelligence, said on Sunday that it would be risky to arm the rebels, "mainly because we just don’t know who they are."
Meanwhile, Russia has sent a third warship to the region.
A Russian guided-missile destroyer, named the Smetlivy, is scheduled to dock at the Syrian port of Tartus in the coming days, according to reports by Agence France Presse.
Moscow claims the ship would only be stopping at Tartus temporarily before heading off for scheduled exercises off Syria's coast, according to reports.
Prior to the Smetlivy, two warships arrived at the Russian naval base in Syria on March 19, according to reports by al Arabiya.
The ships joined up with “a Russian naval reconnaissance and surveillance ship" already anchored in Tartus, the report adds, citing sources within the opposition.
Moscow also reportedly sent elite units of Russian marines and special-operations forces in March to conduct "anti-terrorism" missions in the country.
Russian military advisers are already stationed in the country to help train Syrian troops.