The British-based aid and development charity said international goals to tackle child and maternal mortality were "desperately off track," with four million babies dying within 28 days of birth globally every year.
In a new report, Oxfam and 62 other non-governmental organizations and health groups, also warned that the number of women dying during pregnancy and childbirth has changed little since 1990.
The figures are despite world leaders signing up to the UN millennium development goals to reduce such mortality by 75 percent by 2015.
"How many lives will be needlessly lost before leaders act? Poor people simply cannot afford fees and inaction will continue to deny access to life-saving healthcare for millions," said Oxfam chief executive Barbara Stocking.
The report comes ahead of the UN General Assembly in New York later this month when leaders are expected to consider extending free health services to more poor countries.
The report said in Liberia one in nine children will die before they reach the age of five and less than 20 percent of the rural population have access to health facilities.
In Nepal, a newborn baby dies every 20 minutes and every four hours a woman dies of childbirth-related causes. People living with HIV/AIDS has hit 1.3 million in Mozambique and 60 percent of HIV-infected adults there are women.
In Malawi, one woman in every hundred will die in pregnancy and childbirth, while the entire population of nearly 14 million is looked after by just 266 registered doctors.
"If free health care had been introduced in 2000 when world leaders promised to reduce child mortality by two thirds, the lives of more than two million children could have been saved by now," said Jasmine Whitbread, chief executive of Save the Children.