The second day of artillery, mortar fire and tank shelling left more dead on the Armenian border with Azerbaijan as the EU, US and regional power broker Moscow urged restraint.
Three Azerbaijanis were killed on Sunday and one on Monday, oil-rich Baku's defence ministry said, adding that both sides were using artillery, mortars and tanks in the north part of their border.
The Armenian foreign ministry said the artillery fire from Azerbaijan "receded" later on Monday, claiming Yerevan was "fully controlling" the situation.
The two former Soviet republics have been locked in a simmering conflict for decades over Azerbaijan's separatist region of Nagorno Karabakh, which was seized by ethnic-Armenian separatists in a 1990s war that claimed 30,000 lives.
The international community still views the region as part of Azerbaijan.
The current fighting – hundreds of miles from Nagorno Karabakh – erupted days after Azerbaijan President Ilham Aliyev raised the spectre of war and denounced delays in Karabakh talks.
Each side blamed the other for the current flare-up.
"Armenia's political and military leadership will bear the entire responsibility for the provocation," Mr Aliyev told officials in a meeting.
Armenian Prime Minister Nikol Pashinyan in turn accused Azerbaijan of "provocations" that would "not go unanswered" and his defence minister said Armenian forces would react "including by taking advantageous positions" in Azerbaijani territory.
Armenian Foreign Minister Zohrab Mnatsakanyan on Monday discussed the crisis by phone with the head of the Collective Security Treaty Organization (CSTO), a Moscow-led military bloc.
Before the call, Azerbaijani officials had already said Armenia's "military adventure" was aimed at drawing the CSTO into the fighting.
All-out war between the two countries could potentially drag in regional powers – Armenia's military ally Russia and Azerbaijan's patron Turkey – which compete for geopolitical influence in the strategic region.
Majority-Muslim Turkic-speaking Azerbaijan has received strong backing from its historic ally Ankara.
Turkey's Foreign Minister Mevlut Cavusoglu said Azerbaijan was just trying to "protect its territorial integrity", labelling Armenia's actions "unacceptable" and urging the country to "come to its senses".
Yerevan reacted by condemning Turkey's "provocative attitude," with its foreign ministry accusing Ankara, in a statement, of undermining the "security and stability in the region."
Armenia's military ally Russia – which wields influence on both Baku and Yerevan – expressed "serious concerns" over the crisis, which it said "endangers the region's stability", urging the countries to "show restraint".
Later on Monday, Russian Foreign Minister Sergei Lavrov held phone conversations with his Armenian and Azerbaijani counterparts, urging de-escalation.
The US State Department urged both sides "to stop using force immediately... and strictly adhere to the ceasefire."
The European Union issued a statement calling on both sides "to undertake immediate measures to prevent further escalation."
Mediated by the "Minsk Group" of diplomats from France, Russia and the United States, peace talks between the two sides have been going on since the 1994 ceasefire.
Aliyev threatened last week to withdraw from talks "if they do not yield results" and rejected statements by negotiators that there could be no military solution.
Despite the strong wording, his remarks were widely seen as diplomatic pressure for the stalled talks' intensification.
Armenia, which controls the disputed region, is happy with the status quo in Karabakh that also suits Russia's interests as the Kremlin uses its power-broker's role in asserting its influence in the ex-Soviet republics.
Desperate to restore its territorial integrity by diplomatic means, energy-rich Azerbaijan, whose military spending exceeds Armenia's entire state budget, has repeatedly threatened to take back the territory by force.
Moscow-allied Armenia has vowed to crush any military offensive.
In 2016, deadly clashes in Karabakh nearly spiralled into full-scale war.