The call by a coalition of 140 human-rights groups -- who initially campaigned for monitors to be admitted to the country -- came as the mandate of the much-criticized mission expired and the league was poised to extend it another month.
China and Russia have said they would veto direct Security Council involvement.
A report from the monitors on President Bashar Assad's violent crackdown on the popular revolt against his rule was to be discussed Friday by a six-member league commission before the league's 22 members meet to discuss it Sunday, league officials said.
The Assad regime, which for weeks resisted the monitors' mission to verify Syria's compliance with a November Arab peace plan, said it would agree to the likely extension.
An estimated 125 monitors were still in Syria, while about 40 monitors left because they felt unsafe, an Arab League official in Cairo told The Washington Post.
Eleven monitors were wounded Jan. 9 by pro-Assad demonstrators in the principal port city of Latakia, which government warships and tanks attacked Aug. 14, 2011.
The league official told the Post he expected the monitors' report to be harshly critical of Assad.
But he said, "You cannot call [the mission] a failure."
He cited larger demonstrations in more locations since the monitors arrived as an indication their mission had given a boost to protesters. He also said the mission had increased world attention on the crisis.
The Assad regime has begun issuing visas to foreign journalists -- a step toward the peace plan's demand the regime allow free access to foreign journalists.
It also released about 4,000 prisoners accused of involvement in anti-regime activities, Arab League Secretary-General Nabil el-Araby said.
But the regime carried out only parts of the agreement it had signed, and neither the violence nor the killing stopped, he said. The United Nations said last week the killings had increased since the monitors arrived Dec. 27 after some of the heaviest fighting of the conflict.
The human-rights advocacy group Avaaz said Thursday 746 people had died during the mission.
Activists allege soldiers hold fire when monitors arrive in hot spots and then resume shooting after they leave.
The opposition Local Coordinating Committees said 26 people were killed Thursday.
The November agreement the observers are charged with monitoring compliance with calls for Assad to remove security forces from city streets, release political prisoners, allow free access to foreign journalists and human-rights workers, and begin talks with political opposition groups.