Extreme violence in Central America is sending a surge of refugees fleeing north to Mexico where they are caught between official indifference and yet more danger if they continue to the United States, human rights activists say.

Activists in Tapachula describe a dramatic increase in the number of women and children arriving in southern Mexico this year. Though precise numbers are hard to come by, it seems clear that Mexico has not witnessed such a refugee flow since the 1980s when the region was beset by a series of vicious civil wars involving rightwing dictatorships and leftwing guerrillas.

"There is an undeclared civil war in Central America," said Father Flor Maria Rigoni, who runs a migrant shelter in Tapachula, near the border with Guatemala. "The refugees are coming, but the Mexican institutions aren't taking the problem seriously."

The violence behind today's exodus stems from turf wars between street gangs such as the M-18 and Mara Salvatrucha, the growing power of drug cartels and woefully weak and corrupt state institutions across the region.

Many of the refugees tell stories like that of Mirta, a 24-year-old Honduran woman travelling with her two small sons. After years living in New York, Mirta was so desperate to spend time with her mother she moved her family back to Honduras, even though it had become the most violent state outside a war zone.

The country's murder rate currently hovers around 90 per 100,000 people, compared to one in 100,000 in the UK and five in 100,000 in the US.

The pressure began when masked and armed men she described as "little local narcos" forced her husband to sign over his car and demanded her children's US passports. It became unbearable when they narrowly escaped a kidnapping attempt.

The family fled to Tegucigalpa, the capital, but found themselves in the middle of an open gang war, where they faced regular demands for "war taxes" they could not afford. They moved through El Salvador and Guatemala, but felt vulnerable in both countries, so eventually crossed into Mexico on one of the many rafts made from giant tyres and planks which cross the Suchiate river dividing the two countries, often in full view of the authorities.

Waiting for a decision on her asylum claim, Mirta said she preferred not to think what would happen if it were turned down. Instead she focused on feeding her children. "We just want to find somewhere safe to be and to look for work," she said. "We have received no support. Not even a meal."

Mexico received 860 asylum requests in the first eight months of 2013, about two thirds of them from Hondurans and Salvadorans. About 80% of claims in Mexico are usually turned down.

Direct comparisons of official figures for 2012 were not available, but activists say this year's increase is obvious.

"There are queues to request asylum that never existed before, and many don't apply because they know they could get deported anyway," said Diego Lorente, of the Tapachula-based Fray Matías human rights centre.

The size of the phenomenon is particularly hard to pin down because refugees from violence blend into the broader flow of Central Americans heading to the US for economic reasons.

Many asylum applications are only lodged after migrants have been detained and are being held in centres where Lorente says they suffer obvious mental and physical distress as they wait out the resolution of their cases.

Migration through Mexico peaked in 2005 when the authorities deported around 240,000 Central Americans. Since then a sluggish US economy and tighter controls on the US border have reduced the attractions of going north, as has the knowledge that Mexican drug cartels prey on migrants en route. Reports of kidnapping, rape, murder and forced recruitment are common.

Even so, the Mexican authorities still detained more than 88,000 Central American migrants last year during a journey that has become the preserve of the particularly determined and the desperate.

Emilio is both. "I saw something that I shouldn't have seen," the 43-year-old vendor said to explain his decision to leave El Salvador, his wife and their three children. "Almost all the Salvadorans I have met here are in a similar situation." Emilio shook as he described how he initially tried to lie low but soon realised the gangs were everywhere and his only hope was to leave the country.

Once in Mexico he discounted applying for asylum after an initial interview left him convinced the authorities had no real interest in his story. This left him more focused than ever on joining his brother in the US, whatever the risks he might face on the way.

"I never wanted to leave my beautiful country," he said. "But if I go back now I will die."