Justice, which has been regularly boycotting parliamentary sessions in recent months, accuses the Armenian leader of "usurping power" and "clamping down on freedom of expression."
At the core of the dispute are last year's presidential and legislative polls, which saw the victory of Kocharian and his allies. Justice and other opposition groups claim the vote was rigged and insist that the president be put to a national vote of confidence. The government has denied any wrongdoing in the elections.
Anxious to avoid a political crisis over the disputed elections, Armenia's Constitutional Court last year signaled the constitution could, in principle, be amended in a way that would allow for a national referendum on confidence. But government supporters in the National Assembly (parliament) rejected the idea, saying it had no legal basis.
One of the three partners in the ruling coalition, the Dashnaktsutyun Armenian Revolutionary Federation, yesterday demanded that the opposition cease to question Kocharian's legitimacy. In return, the nationalist party said, Justice and its allies should be given seats in the National Security Council to have a say in domestic affairs.
A Dashnaktsutyun statement said only dialogue would help prevent what it called "open confrontation."
But Justice leader Demirchian yesterday rejected the offer, saying the opposition would accept nothing less than the confidence vote.
"How could we possibly talk about dialogue when opposition members are being arrested? Arrests are actions inherent with a junta. A real dialogue would have been to call for a national referendum on confidence [in Kocharian]. However, there is still room for introducing constitutional amendments that would pave the way for such a referendum," Demirchian said.
Demirchian went on to say the opposition was determined to pursue its anti-Kocharian campaign regardless of offers made on behalf of the government and despite counter-steps taken by the authorities.
"I understand the fears of Dashnaktsutyun. The situation in the country is indeed tense. But the opposition has never asked for any government post," Demirchian said. "What we want is that constitutional order in the country be restored."
On 31 March, the Prosecutor'-General's Office in Yerevan launched criminal proceedings against Justice and its allies, which it blamed for a series of recent unsanctioned rallies that purportedly called for a violent change of regime and using what it said was "offensive language" against senior government officials.
The Prosecutor-General's Office yesterday said Suren Sureniants of the opposition Hanrapetutyun (Republic) party -- a leading member of the Justice alliance -- was arrested in connection with the investigation.
Hanrapetutyun spokesman Artak Hakobian told RFE/RL's Armenian Service that Sureniants was arrested in a village nearby Yerevan and brought to the capital for questioning. The Prosecutor-General's Office said no formal charges had been brought against him yet.
Hakobian also said opposition activists were being detained in many Armenian regions.
"Today we've been receiving phone calls from our people in Yeghvard, Charentsavan, Stepanavan, Vanadzor, and Gyumri. People are being either summoned or taken to the police. Some of them are being released, some are being put into custody," Hakobian said.
Addressing reporters in Yerevan today, police chief Nerses Nazarian said nearly 40 opposition activists have been apprehended. He did not say whether charges were brought against them or how long they would remain in custody.
Meanwhile, representatives of ruling coalition parties have justified the detentions.
Dashnaktsutyun member Vahan Hovanessian yesterday said authorities "have the right to take necessary steps to isolate people transporting weapons and other instruments that could be used in possible clashes."
Republican Party member Tigran Torosian told RFE/RL's Armenian Service that harassment of the opposition will stop once it ceases its anti-Kocharian campaign.
Opposition activists yesterday took to the streets of central Yerevan to demand that the president step down and that a national referendum be organized.
Estimates put the number of participants at between 3,000 and 8,000.
Media reports say unidentified youths smashed cameras belonging to several journalists at the rally near the Matenadaran Library. Also, eggs and stones were thrown at the protesters from nearby balconies. No serious clashes were reported, however.
National Unity party leader Artashes Geghamian, who led yesterday's protest, claimed the authorities were unwilling to compromise with the opposition.
"Had authorities called off police from the Matenadaran area, agreed to come with us to meet with voters, or shown their goodwill [in any other from], that would have been a starting point for cooperation. But instead, they attempted to close bridges and roads leading to Yerevan," Geghamian said.
Despite uneasy relations stemming from last year's presidential polls, Geghamian and Justice leader Demirchian recently forged an alliance aimed at securing Kocharian's ouster.
(Ruzanna Khachatrian and Armen Doulian of RFE/RL's Armenian Service contributed to this report.)