Hajiyev was speaking after his country launched military action in Karabakh, a mountainous region internationally recognised as Azerbaijani, part of which is run by breakaway ethnic Armenians who say it is their ancestral homeland.
Armenia on Tuesday denied having any forces in the area.
However, many Armenians have in the past volunteered to fight for Nagorno-Karabakh.
Hajiyev said Azerbaijan would only be ready to talk to the Karabakh Armenians once they had raised the white flag and disarmed.
He said Azerbaijan had no military objectives in neighbouring Armenia.
"The intention of Azerbaijan is to close a chapter of animosity and confrontation," he said.
"Enough is enough. We cannot tolerate any longer having such armed forces on our territory and also a structure which, on a daily basis, challenges the security and sovereignty of Azerbaijan."
He said Azerbaijan believed that what he called its anti-terrorism action would achieve its strategic goal of ensuring full sovereignty over its territory.
Ethnic Armenian officials said two civilians were killed and 23 wounded amid heavy artillery fire around Nagorno-Karabakh's capital.
Azerbaijan's authorities also accused Armenian forces of killing a civilian, which brought the civilian death toll of Tuesday's hostilities to at least three.
The Azerbaijani defence ministry announced the start of the operation hours after four soldiers and two civilians died in landmine explosions in the Nagorno-Karabakh region.
The reports raised concerns that a full-scale war over the region could resume between Azerbaijan and Armenia, which fought heavily for six weeks in 2020.
Ethnic Armenian officials in Nagorno-Karabakh said in a statement that the region's capital Stepanakert and other villages were "under intense shelling".
Nagorno-Karabakh human rights ombudsman Geghan Stepanyan said two people were killed in the firing - including one child - and 23 were wounded.
At least eight of those injured also are children, according to Stepanyan.
The Azerbaijani Prosecutor General's Office said Tuesday that Armenian forces fired at Shusha, a well-known city in Nagorno-Karabakh under Azerbaijan's control, from large-caliber weapons, and one civilian was killed there as a result.
Although Azerbaijan said the operation was limited to military targets, the defence ministry said that "humanitarian corridors" had been created to allow people to leave "the danger zone".
with AP
