President Donald Trump last month ordered that asylum be denied to anyone who enters the country illegally from Mexico, but a federal judge in San Francisco blocked him.
The migrants breached the US-Mexico border with the hopes of avoiding months of wait times as thousands apply for asylum at American Port of Entry across the region.
When asked how the group came up with the $50,000 figure, organizer Alfonso Guerrero Ulloa of Honduras, said they chose that number as a group. "But it is a small sum compared to everything the United States has stolen from Honduras", he claimed.
The groups arrived separately at the consulate, both unaware of the other's demands, the San Diego Union-Tribune reported.
The migrant group gave the consulate 72 hours to respond to their demands.
A confrontation with rock-throwers from Mexico led to US agents firing tear gas into Mexico on November 25 and a five-hour closure of the nation's busiest border crossing. The US is processing up to about 100 claims a day at the San Diego crossing, which is creating a backlog.
US immigration authorities say the number of people expressing fear of returning home when they are stopped at the Mexican border spiked in the previous year.
The San Diego Union-Tribune has reported that others have been able to cross in the USA illegally or moved to other parts of Mexico.
The girl was taken to a local holding facility and is now in the custody of U.S. Immigration and Customs Enforcement officials as authorities try and find her mother. "Our sacred texts tell us to tear down walls, to welcome the immigrant and to treat everyone as if they are God's children", said Rev. Dr. Liz Theoharis, who held a sign that read "El Amor No Conoce Fronteras", Spanish for love knows no borders.
Two migrant caravans have demanded entry into the USA from Honduras or $50,000 to return home as well as faster asylum seeker processing and larger migrant entry numbers. The "credible fear" claims accounted for 18 percent of all people arrested or stopped at the Mexican border in the latest period, up from 13 percent a year earlier.