The authorities in Nepal have rejected international criticism of the king's decision to seize absolute power.
Mr Giri says the government has no choice but to take tough action
They say the move to implement a state of emergency was necessary to stop the country sliding into chaos after years of bloody conflict with Maoist rebels.
Newly-appointed deputy premier Tulsi Giri told the Reuters news agency that there is a "chaotic law and order situation because of terrorism".
On Monday the US, and EU nations recalled their ambassadors to Nepal.
Mr Giri told Reuters that Nepal was acting no differently from the US after the World Trade Centre attack in September 2001, or from India in its fight against militants in Kashmir.
Security is heavy in Kathmandu for the Maoist blockade
"Every country has a problem which it is trying to solve," he said, "but then it's not justice that you make comments on how Nepal is dealing with it."
Mr Giri said the government would have no choice but to pursue the guerrillas if they kept rejecting peace talks. "If they co-operate, it's OK. Otherwise, what's the alternative?" he asked.
On Monday US State Department spokesman Richard Boucher said Washington was "deeply concerned by developments in Nepal".
Recalled for consultations
King Gyanendra assumed direct control nearly two weeks ago, saying the former government had failed to tackle Maoists, during whose nine-year insurgency 11,000 people have been killed.
Reflecting their governments' opposition to the royal coup, the US, the UK, France and others all recalled their ambassadors for consultations on Monday.
The king took over nearly two weeks ago
Mr Boucher said: "King Gyanendra's dismissal of the government, declaration of a state of emergency, detention of politicians, human rights workers and students and the suspension of fundamental constitutional rights is a step away from Nepal's path toward democracy."
British Foreign Secretary Jack Straw, who is visiting Pakistan, said Britain "strongly" supported constitutional monarchy and multi-party democracy in Nepal.
"We continue to call upon the Maoists to end their violence and for both sides to return to the negotiating table."
India also urged Nepal to take "immediate steps" to restore multi-party democracy.
The king moved to ease some restrictions on Monday, when he freed former premier Surya Bahadur Thapa, as well as a prominent lawyer and a senior leader of the country's biggest communist party.
But he also consolidated his power by appointing Mr Giri and another former prime minister, Kirti Nidhi Bista, as his deputies in his new cabinet.
They were both in power during the last time that Nepal was directly ruled by a king and are seen as staunch royalists.
Meanwhile the kingdom's biggest party, the Nepali Congress, is calling for a nationwide, non-violent struggle for the restoration of democracy from this Friday. Details are still being worked out.
A transport blockade launched by Maoist rebels entered its fourth day on Tuesday, with traffic movement reported to be lower than normal and prices rising in the capital, Kathmandu.
The rebels say that the royal coup has forced them to abandon earlier negotiation demands and implement the blockade as a means of abolishing the monarchy.