Berisha accused the socialist opposition of wanting to trigger "a Tunisian-style scenario for Albania" by staging "a coup to seize power by force," AFP reported.
Tens of thousands of people took to the streets for an anti-government protest called by the socialist opposition on 21 January. The demonstration ended with violent clashes between protesters and the police, and three people were killed.
Albania's President Bamir Topi and Western envoys urged warring political parties to settle their differences and called on security forces to launch investigations into the three people deaths.
Prosecutors said on Sunday that police had not yet acted on arrest warrants issued for six republican guardsmen suspected of carrying out the shootings in Friday's confrontation.
Berisha and opposition Socialist Party leader Edi Rama blamed one another for the deaths, with each side promising new rallies in an escalating political row.
"Restoring political dialogue, respect for the institutions of the state and the expression of maturity and balance is of a vital importance for the present and European future of Albania," a statement from President Bamir Topi and US and European Union ambassadors said on Saturday evening.
They said it was "indispensable that law enforcement institutions cooperate with each other to conduct a transparent, professional and unbiased investigation".
The prime minister said he would not allow fresh violence.
"Every attempt from him [Rama] for violence against institutions will have an exemplary punishment," Berisha told a government meeting before his lawmakers approved a parliamentary investigation into the violence. "There will be zero tolerance for those who touch any institution."
Rama told Reuters he was committed to peaceful action.
"The opposition has nothing in common with violence, weapons or internal impulses to take power through the streets. We want to move forward with peaceful resistance and open the way to a new possibility for a democratic Albania," he said.
The opposition Socialists refused to accept the results of 2009 elections which gave Berisha, Albania's dominant post-Communist politician, a second four-year term and accused his government of corruption and vote fraud (see EurActiv LinksDossier on EU-Albania relations). Deputy Prime Minister Ilir Meta resigned this month amid corruption charges.
One of Europe's poorest countries, Albania is part of NATO but the European Union rejected its application last year to become an official candidate for membership of the bloc, urging it to fight corruption and establish a functioning democracy and the rule of law.
In a move to bolster support, Berisha on Saturday gave a bonus of one month's wages to security officials who patrolled the protest on Friday, and four months' wages for police officials who were wounded.
Security officials have placed coils of barbed wire on the ground around government buildings on the capital's main boulevard.
A planned opposition rally on Sunday was delayed pending the completion of the last two of three funerals. One funeral, with Rama in attendance, was broadcast live on Albanian television.
The opposition Socialists scheduled a rally for next Friday at the same location in front of Berisha's office, Reuters reported.
