Armenian and Azerbaijani forces have clashed over the disputed region of Nagorno-Karabakh.
Two Azeris were killed and one Armenian was injured in the ceasefire breach, Armenian Foreign Minister Vardan Oskanyan said.
Azeri authorities told the BBC Armenia had provoked the clashes to divert attention from its domestic problems.
Eight people died during clashes with police in the Armenian capital Yerevan on Saturday, after disputed elections.
Tuesday's border clash happened in the Mardakert area of northwestern Nagorno-Karabakh, a disputed Armenian-controlled enclave inside Azerbaijan, Itar-Tass news agency reported.
A ceasefire was agreed in 1994 after Armenia took control of the territory in a full-scale war.
Azerbaijan's President Ilham Aliyev has said his country is ready to re-take the region by force, and has been buying the military hardware and ammunition to do so.
Also on Tuesday, Armenian police arrested 30 opposition activists accused of causing Saturday's clashes with police in Yerevan, which led to a state of emergency being called.
The opposition accuses the authorities of having rigged last month's presidential election.
The border fighting comes amid a state of emergency in Yerevan
Armenia's prosecutor-general said the 30 detained activists had been arrested "for using violence, causing danger for the life and health of police".
The election was officially won by PM Serzh Sarkisian, who beat opposition candidate Levon Ter-Petrosian.
Official results gave Mr Sarkisian 53% of the vote in the 19 February election, with Mr Ter-Petrosian on 21.5%.
International observers judged the election to be generally democratic but noted some problems with the vote count.
Two pan-European bodies, the Council of Europe and the Organisation for Security and Co-operation in Europe (OSCE), have voiced concern about the situation in the former Soviet republic.
Armenia's constitutional court has now started considering the opposition's challenge to the election results - although government ministers have told their opponents to accept defeat.
Mr Ter-Petrosian vowed to continue the protests
Earlier this week, Mr Ter-Petrosian, a former president, vowed to continue protesting against the result of the poll, saying it was rigged.
He warned that there could be years of political conflict ahead.
He expressed regret about the eight people who died on Saturday.
But he blamed the government for the pitched battles between police and protesters, who had set up barricades in the city centre.
The authorities said they had to restore order after 11 days of mass demonstrations which they had repeatedly warned were illegal.
Outgoing President Robert Kocharian declared a state of emergency was in force until 20 March.