Dahal, a former Maoist rebel leader, says Rookmangud Katawal has failed to integrate his former fighters into the military, a requirement of the peace deal that ended their 10-year conflict with the government.
Navin Ghimire, the home ministry spokesman, said police and soldiers had been deployed on the street of the capital to prevent further protests.
The authorities banned demonstrations and rallies in areas of Kathmandu as it appeared that the political standoff could unravel the country's fragile stability established in the three years since the peace deal.
Political parties have been holding talks in an attempt to form a new coalition government, but the communist party has stayed away.
Dahal, whose party is the largest in parliament but does not have an absolute majority, told reporters on Wednesday that his party would join a new government only if the president reversed his decision to block the army chief's dismissal.
The president, who was elected by parliament, belongs to the Nepali Congress party, the country's second-largest party after the Maoists.
Communist party supporters warned that they would continue their demonstrations and block a new prime minister from being voted in.