The fighting, which each side blamed on the other, left more than 170 soldiers dead and threatened to drag Turkey - Azerbaijan's key backer - and Armenia ally Russia into a wider conflict at a time of already high geopolitical tensions.
A ceasefire was agreed between the two sides late on Wednesday, a senior Armenian official said.
Moscow, which has a self-defence pact with Armenia and a military base in the country but also strives for friendly relations with Azerbaijan, claimed credit for the deal.
"We welcome the cessation of hostilities between Azerbaijan and Armenia and will continue to work with the parties to seek to cement it," tweeted US Secretary of State Antony Blinken.
Before the ceasefire was announced, Armenia's Prime Minister Nikol Pashinyan said Azerbaijani forces had struck and seized several Armenian settlements along their shared border, in territory beyond the disputed Nagorno-Karabakh region.
Baku said it was responding to "provocations".
A monitoring mission from the Moscow-led Collective Security Treaty Organisation arrived in Armenia's capital Yerevan on Thursday and held talks with defence officials, Tass news agency said.
Russia and Armenia are members but Azerbaijan is not.
"The international community must remain fully committed to a peaceful settlement between Armenia and Azerbaijan," UN Assistant Secretary-General Miroslav Jenca said on Thursday.
Russia said it was seeking to reverse any shift in the military balance of the region that had occurred as a result of the fighting.
"We are in close contact with both countries, so as to arrive at a sustainable ceasefire and the return of Azerbaijani and Armenian military to their positions of origin," Russia's ambassador to the UN, Vassily Nebenzia, told the 15-member Security Council.
Armenia's deputy defence minister told Reuters the conflict risked spilling over into a full-blown war, while some analysts said Baku was trying to take advantage of Russia's war in Ukraine to advance its position.
"This week's events are also a stark reminder that tensions between Armenia and Azerbaijan also have the potential to destabilise the region," the UN's Jenca said.
The fighting was the deadliest in almost two years since a six-week war in 2020 left thousands dead and Azerbaijan made significant territorial gains in and around Nagorno-Karabakh.
