The ceasefire in the occupied Nagorno-Karabakh region is under severe strain following Armenia's repetitive violations.
Azerbaijan's President Ilham Aliyev has urged the international community to impose sanctions on Armenia.
In a televised speech on Tuesday, Aliyev said that Armenian army is involved in "massacres" of civilians, adding Armenia should respect the international law.
Aliyev expressed the resolve that Azerbaijan would liberate its lands from the Armenian occupation, adding the Azerbaijani army has liberated Zangilan city.
In addition, six villages of Fuzuli, seven villages of Jabrayil, five villages of Khojavend and six villages of Zangilan have also been liberated.
Aliyev's statement came as a ceasefire in the mountain territory of Nagorno-Karabakh was under severe strain on Tuesday after fierce new clashes between Azerbaijani and Armenian forces.
The ceasefire, agreed on Saturday, has had little impact on fighting that began on September 27, despite concerns it could spark a wider conflict involving Russia and Turkey.
Azerbaijan says two civilians killed in Armenian attacks
At least two civilians were killed and one injured in attacks by Armenia on civil settlements in Azerbaijan, Baku’s Foreign Ministry said on Tuesday.
"URGENT! 3 civilian casualties in Tartar. Anar Isagli (26) and Anar Guliyev (36) killed, Murov Shabanov (48) injured as artillery strikes by #Armenia's forces hit their home," the ministry said on Twitter.
Azerbaijan’s Prosecutor General’s Office said the Tartar province has been subjected to Armenian forces’ missile and artillery fire from various directions since early Tuesday.
It also announced that since the start of hostilities, Armenian artillery and missile attacks on Azerbaijani settlements have killed at least 61 civilians and injured 291 others as of midday Tuesday.
A total of 1,941 houses, 90 apartments and 382 residential and public buildings have been damaged and made unusable because of Armenian attacks.
Armenian Defense Ministry spokeswoman Shushan Stepanian also reported “intensive fierce battles” on Tuesday morning in the southern areas of the conflict zone, and alleged that Azerbaijani forces were using aviation and artillery in the northern sector.
Several hundred people have been killed since September 27 in fighting involving drones, warplanes, heavy artillery, tanks and missiles, raising fears of a humanitarian crisis and concerns about the security of oil and gas pipelines in Azerbaijan.
The new ceasefire appears to have had no more effect on fighting than an earlier deal brokered by Russia that failed.
Azerbaijan wants an end to Armenian occupation of Nagorno-Karabakh.
Azerbaijan's defence ministry reported fighting in several areas, including Nagorno-Karabakh close to the line of contact dividing the sides.
It said Armenian forces were shelling the Azerbaijani regions of Tartar and Aghdam.
Azerbaijan said its foreign minister, Jeyhun Bayramov, would hold talks with US Secretary of State Mike Pompeo and the Minsk Group in Washington on Friday, but gave no details.
Russia's permanent representative to the United Nations said the Security Council had discussed the conflict on Monday. Asked about the possibility of UN observers going to the region, he said that would require a mandate from the Security Council.
"This is not a quick process," the envoy, Vasily Nebenzya, was quoted as saying by TASS. He suggested any observer mission might involve the OSCE.
Putin, Macron want Armenia, Azerbaijan to relaunch talks
Russian President Vladimir Putin and French counterpart Emmanuel Macron discussed the situation in Nagorno-Karabakh during a phone call, their offices said in statements on Tuesday.
The two leaders, who co-chair with the United States the so-called Minsk group in charge of mediating between Armenia and Azerbaijan, said they agreed the two South Caucasian countries should relaunch "substantial negotiations", the Elysee said.
Armenia and Azerbaijan said on Tuesday their foreign ministers would meet US Secretary of State Mike Pompeo in Washington on Friday in efforts to end the heaviest fighting in and around the enclave of Nagorno-Karabakh since the 1990s.
Minsk Group is 'brain-dead'
Turkey's parliament speaker has criticised the OSCE Minsk Group over ongoing Azerbaijan-Armenia crisis, saying that the group is "brain-dead".
"The OSCE Minsk Group, which has not been able to find a solution to the Nagorno-Karabakh issue for 30 years, has been brain-dead," said Mustafa Sentop at the Azerbaijani parliament in the capital Baku.
The OSCE Minsk Group - co-chaired by France, Russia , and the US - was formed in 1992 to find a peaceful solution to the conflict, but to no avail.
Armenia has "become a regional and a global problem", Sentop said, noting: "Deadlock in the Caucasus will continue as long as Armenia's occupation in Nagorno-Karabakh and surrounding areas continues."
As part of his three-day official visit to hold talks on the ongoing Upper Karabakh conflict, Sentop also met with Azerbaijan's Foreign Minister Jeyhun Bayramov.
Sentop and Bayramov discussed the ongoing crisis between Azerbaijan and Armenia, and addressed Azerbaijan's operations to rescue its occupied lands.
Relations between the two former Soviet republics have been tense since 1991, when the Armenian military occupied Upper Karabakh, an internationally recognised territory of Azerbaijan.
Turkey has supported Baku's right to self-defence, and demanded a withdrawal of the occupying forces.