The UNHCR's Georgia office said on Facebook that anyone "requesting international protection in Georgia has access to a fair and effective asylum procedure".
The Saudi women began posting tweets about their situation on Tuesday, initially not revealing their identities.
Wafa Alsubaie, said in a video that their father and brothers were already in Georgia and searching for them.
"We fled oppression from our family because the laws in Saudi Arabia (are) too weak to protect us," she said.
The UNHCR's Georgia office said on Facebook that anyone "requesting international protection in Georgia has access to a fair and effective asylum procedure".
Saudi Arabia is one of the world's most restrictive countries for women.
In a similar case in March, another two Saudi sisters aged 20 and 18 who were marooned in Hong Kong arrived in a safe third country after securing humanitarian visas as they sought sanctuary from an abusive family.
At the beginning of the year, 18-year-old Saudi woman Rahaf Mohammed al-Qunun drew global attention with her dramatic escape from an allegedly abusive family, gaining refugee status in Canada.
Many Saudi women who flee overseas have spoken to media and rights groups of persuasive and coercive tactics used by Saudi officials and family members to pursue those who escape.
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