Honduras is set to host one of the world's most radical neo-liberal economic experiments under a plan to build from scratch the rules, roads and rafters of a "charter city" for foreign investors.

The Central American nation hopes the plan for model development zones, which will have their own laws, tax system, judiciary and police, will emulate the economic success of city states such as Singapore and Hong Kong.

But even as the government signed a "memorandum of understanding" with a group of international investors on Tuesday, opponents tried to lodge a suit at the supreme court for the arrangement to be declared illegal because the "state within a state" risked undermining national laws, sidestepping labour rights, worsening inequality and creating a modern-day enclave that impinged upon the territory of indigenous groups.

The Honduran president, Porfirio Lobo – a landowner from the rightwing National party – has given his full backing to the plan, which was inspired by US economic advisers.

During the signing ceremony, government officials said the initial $14m phase of the project would start in October and create 5,000 jobs in the first six months and 40 times that number in the future – a major incentive in a country where one in four of the workforce are unemployed.

"This is the most important project in half a century for Honduras," said Carlos Pineda, head of the Commission for the Promotion of Public-Private Partnerships, which represented the government at the signing of a memorandum of understanding with the business consortium NKG.

Details of the arrangement remain sketchy. Three possible locations were mentioned – Sula valley, Agalta valley and the southern region of Honduras – and the initial investments seemed small compared to the scale of the ambition.

The plan appears to have been thrown together in the space of less than a year, partly to boost the economy and partly to make Honduras more attractive to foreign investors who fear crime (Honduras has the world's highest murder rate) and political instability (Lobo was elected following a coup d'etat in 2009).

It is the realisation of a proposal for "charter cities" proposed by the US economist Paul Romer, a graduate of the University of Chicago school of economics, who is currently professor at the Stern School of Business at New York University.

Citing Hong Kong as an example, Romer argues that cities based on a "charter" of strong, pro-business laws and institutions are the key to rapid growth, particularly when they can act as international gateways to larger regions such as China. In countries that lack such fundamentals at a state level, he proposes the creation of special zones where they can be established from nothing.

Soon after Romer visited Tegucigalpa at the start of the year, the Honduran congress approved an enabling bill for the creation of economic development zones. Lobo has reportedly taken fact-finding delegations to Hong Kong, Singapore and Dubai to look at possible models.

None of those cities, however, attempted the urbanisation from scratch now being eyed in Honduras.

Proponents say this is an advantage because the governance systems and rights can be designed. "It's easier to create something new that will be healthy and safe than to go and deal with the serious problems that exist across the whole nation," said Mark Klugman, a government adviser.

But the idea has provoked controversy in a country already suffering from one of the worst levels of inequality in the world.

Critics say it will allow a foreign elite to set up a low-tax, sympathetically regulated enclave where they can skirt labour standards and environmental rules.

"This would violate the rights of every citizen because it means the cession of part of our territory to a city that would have its own police, its own juridical power, and its own tax system," said Sandra Marybel Sanchez, who joined a group of protesters who tried to lodge an appeal at the supreme court.

Ismael Moreno, a correspondent for the leftwing Nicaraguan magazine Envio, compared the charter cities to the banana enclaves, which were run on behalf of a foreign elite. He also spelled out the environmental risks, particularly if one of the development sites is the Sico valley, an area of virgin forest on the Mosquito Coast.

"This model city would end up eliminating the last agricultural frontier left to us," he wrote.

Indigenous and ethnic groups also expressed hostility to the move. Miriam Miranda, president of the Fraternal Black Organisation of Honduras, said a project in the Puerto Castilla – close to one of the three sites – would threaten the continuity of the Garifuna people and culture.

Michael Strong, an NKG executive, insisted, however, that the project would be a driver for poverty elimination. "The main goal of our project is to create the basis for a safe and prosperous future for Hondurans," he was quoted as saying by local media.