According to AFSC, 30 religious leaders were arrested by border patrol agents.
More than 300 people, many the leaders of churches, mosques, synagogues and indigenous communities, participated in the demonstration at San Diego's Border Field State Park, which borders Tijuana, Mexico.
Homeland Security officials said the $50,000 demand put the lie to claims that caravan members are legitimate asylum-seekers.
Border Patrol spokesman Eduardo Olmos said 31 people were arrested on suspicion of trespassing by the Federal Protective Service and one was arrested by the Border Patrol for assaulting an agent. The Border Patrol calls it "an enforcement zone".
Another group of migrants also made the trek to the consulate to present a different demand, asking that US officials speed up the processing of people demanding asylum at the ports of entry. They were handcuffed and led away by federal agents upon entering a restricted area in front of the fence. "We're calling on the U.S.to respect the rights of migrants", Joyce Ajlouny, general secretary of AFSC, told NBC News.
Two migrant caravans have demanded entry into the US from Honduras or $50,000 to return home as well as faster asylum seeker processing and larger migrant entry numbers.
Thousands of migrants are living in crowded shelters in Tijuana after travelling from Central America to escape poverty and violence.
U.S. immigration officials say these claims, most of which are accepted, exploit a legal loophole allowing migrants to enter the USA while they await a court hearing on their asylum case. They were a group of about 50 migrants with demands that included faster asylum processing and increased entry for asylums seekers. - The United States embarked Friday on a policy of automatically rejecting asylum claims of people who cross the Mexican border illegally in a bid to deter Central American migrants and force Mexico to handle them.
USA migrant activist Pat Murphy, who heads a Catholic-run migrant shelter in Tijuana, said demonstrators meant to carry out a blessing at the border fence to start a week of action called "Love Knows No Borders: A moral call for migrant justice".
Customs and Border Protection Commissioner Kevin McAleenan says the claims are straining resources.