The three-member commission reported its most recent findings of rights abuse at the hands of Syrian President Bashar Assad's government to the United Nations Friday, The New York Times reported.
The commission said initially people fleeing Syria left by themselves or in small groups, but now entire clans and villages are leaving together.
"There are people coming out in greater numbers," said Karen Koning AbuZayd, a commission member. "People are now coming out in whole groups."
The commission's chairman, Sergio Pinheiro, said refugees told them military forces threatened to shell their villages if suspected insurgents hiding in their midst did not surrender.
The United Nations refugee agency has reported 17,000 Syrian refugees in Turkey, 16,000 in Lebanon and at least 8,000 in Jordan.
Meanwhile, the U.N. Human Rights Council Friday adopted a resolution on Syria, RIA Novosti reported.
The resolution stated the Human Rights Council strongly condemns the "sharply escalating widespread, systematic and gross violations of human rights and fundamental freedoms perpetrated by the Syrian authorities."
Russia, China and Cuba voted against the resolution.
"The adoption of the biased and inadequate resolution goes against the efforts of the international community on stabilizing the situation in Syria," the Russian Foreign Ministry said Saturday.