Protesters branded the law an "affront to the heritage" of the country.
Legislators last week ratified the disputed laws - originally approved last year - which will facilitate the construction of hotels and restaurants near historic sites.
The laws were modified three days later affording regional governments a say in their implementation.
But local leaders say the concessions are not enough to protect prominent sites such as Machu Picchu. They have also threatened an indefinite regional strike if congress does not dismiss both laws.
Efrain Yepez, a regional assembly leader, said: "The reformed law did not involve Cuzco. It has gaps, so we continue the protests."
Jorge del Castillo, the cabinet chief for Alan Garcia, Peru's president, called the protests "irresponsible" and said that an extended strike could jeopardise Cuzco's role in this year's Asian-Pacific Economic Cooperation summit.
Machu Picchu, a 15th-century site atop an Andes mountain peak - 2,500m-high - attracts about 800,000 tourists a year, most of whom travel there by train.
The city was named a Unesco World Heritage Site in 1983.