- Three years ago, Azerbaijan recaptured territories in and around Karabakh that had been held by Armenia since 1994.
- Since December, Azerbaijan has mounted an effective blockade of the only route into the enclave from Armenia, known as the Lachin Corridor.
Azerbaijan's defence ministry says it has begun "anti-terrorist" operations in areas of its Nagorno-Karabakh region under ethnic-Armenian control.
Tensions in the South Caucasus have been high for months around the breakaway enclave, recognised internationally as part of Azerbaijan.
Air raid sirens and mortar fire were heard in Karabakh's main city.
Eleven Azerbaijani police and civilians have been reported killed in a mine blast and another incident.
Defence officials in the breakaway region said the Azerbaijani military had "violated the ceasefire along the entire line of contact with missile-artillery strikes". Other Karabakh representatives spoke of a "large-scale military offensive".
The two neighbours, Azerbaijan and Armenia, have gone to war twice over Nagorno-Karabakh, first in the early 1990s after the fall of the Soviet Union and again in 2020.
Three years ago, Azerbaijan recaptured territories in and around Karabakh that had been held by Armenia since 1994.
Since December, Azerbaijan has mounted an effective blockade of the only route into the enclave from Armenia, known as the Lachin Corridor.
On Tuesday, the defence ministry in Baku accused Armenian forces of "systematic shelling" of its army positions and said it had responded by launching "local, anti-terrorist activities... to disarm and secure the withdrawal of formations of Armenia's armed forces from our territories".
It insisted it was not targeting civilians or civilian buildings, and that "only legitimate military targets are being incapacitated by the use of high-precision weapons".
In a brief televised address, Armenian Prime Minister Nikol Pashinyan rejected claims that his military was involved and accused Azerbaijan of launching a "ground operation aimed at ethnic cleansing of Karabakh Armenians".
The sound of artillery and gunfire could be heard on Tuesday from the Karabakh regional capital Khankendi, known as Stepanakert by Armenians.
An estimated 120,000 ethnic Armenians live in the mountainous enclave.
Journalist Siranush Sargsyan said residential areas of the city had been hit, including a building next door to her.
Karabakh's human rights ombudsman said two civilians, including a child, had been killed and several other children were among the wounded.
Officials in Armenia added that as of 14:00 local time (10:00 GMT), the situation on the country's own borders was "relatively stable".
Russia's foreign ministry said it had been warned of the Azerbaijani offensive only minutes in advance and urged both countries to respect a ceasefire signed after the war in 2020. The EU's regional special representative, Toivo Klaar, said there was "urgent need for immediate ceasefire".
The fragile truce that brought the six-week war to an end in 2020 had come under increased pressure in recent months.
South Caucasus commentator Laurence Broers said on Tuesday the Armenian population in Karabakh had been weakened by the blockade and the Azerbaijan operation had been launched "seemingly to retake Armenian-populated Karabakh in its entirety".
Hikmet Hajiyev, special adviser to Azerbaijan's President Ilham Aliyev, called on the separatist ethnic-Armenian administration to "dissolve itself".
Some 3,000 Russian peacekeepers were deployed to monitor the 2020 ceasefire but Moscow's attention has been diverted by its full-scale invasion of Ukraine.
The Armenian prime minister said recently that Russia was "spontaneously leaving the region". Azerbaijan has meanwhile had strong support from its ally Turkey.
Azerbaijan had denied building up troop numbers in the region. On Monday, it allowed aid from the International Committee of the Red Cross into Karabakh on two roads, one via the Lachin Corridor from Armenia and the other on Azerbaijan's Aghdam road.
There had been hopes that tensions might subside, but then Azerbaijani officials said six people were killed, including four police, when their vehicle went over a landmine in the Khojavand area, which was recaptured during the 2020 war.
The defence ministry released images of the destroyed vehicle, but ethnic Armenian officials in Karabakh said it was Azerbaijan's military that had violated the ceasefire.