Some 70,000 Oaxaca teachers and supporters have been on strike in the city for five months demanding higher pay and the resignation of the state governor.
A statement from the Mexican interior ministry demanded "the immediate hand-over of the streets, plazas, public buildings and private property" taken over by protesters.
President Vicente Fox ordered federal police to Oaxaca on Saturday after a US cameraman for the Indymedia independent media website and two Mexicans were shot dead on Friday.
Fox's office said in a statement that protesters were "undermining order and peace."
The protesters' barricades on Friday had blocked main access routes to the state capital, which has a population of about 600,000.
The teacher protests began in May, and in June angry demonstrators and their supporters took over government offices demanding the resignation of state Governor Ulises Ruiz, a member of the long-ruling Institutional Revolutionary Party (PRI), whom they say has gone too far in putting down demonstrations.
Florentino Lopez, a spokesman for the federation of civic groups supporting the teachers, said "people are more angry than they are afraid.
"People are pouring out into the streets. There are some 10,000 people at all of the barricades," which he said would be defended.
US journalist and cameraman Brad Will was killed on Friday after being shot in the chest in Oaxaca, according to Lopez.
Teacher Emilio Alonso was fatally shot in San Bartolo Coyotepec, 15 kilometres (10 miles) from Oaxaca, while waiting for the governor to arrive, his wife told the local Universitaria radio station.
Late on Friday, authorities also announced the violence had claimed the life of a man identified as Esteban Zurita Lopez.
At least 11 people were injured by gunshots in the violence, including Mexican photographer Oswaldo Ramirez of Milenio magazine, who was shot in the leg, Lopez said.
Most of the residents of Oaxaca state are native Americans of 15 different ethnic groups.
The Fox administration has little sympathy for Ruiz, a controversial governor from an opposition party. But Ruiz has support from his powerful party, and Fox's conservative PAN party lacks a majority in Congress and needs to maintain good relations with Ruiz's party.
The city of Oaxaca, a UNESCO World Heritage Site founded by Spanish conquistadors in the 16th century, has been largely paralysed by the protests.

Copyright AFP (Agence France-Presse), 2006