A man looks at a house damaged during fighting in Batken, southwestern Kyrgyzstan, Saturday, Sept. 17, 2022. AP
"The total number of dead as a result of the armed conflict in the Batken (border) region is 36," the health ministry said in a statement.
A further 139 people had been wounded in the fighting on the southwestern border, it said.
The previous toll given by the ministry was 24 dead.
Similarly, Tajikistan said on Sunday, on it's official foreign ministry Facebook page, that 35 of its citizens were killed in the border clashes including civilians, women, and children.
Russian President Vladimir Putin on Sunday called for "no further escalation" between Kyrgyzstan and Tajikistan.
In phone calls with the leaders of the Central Asian nations, Putin also urged them to "take steps to resolve the situation as soon as possible by exclusively peaceful, political and diplomatic means". according to a statement from the Kremlin.
Both Kyrgyzstan and Tajikistan are part of the Russia-led Collective Security Treaty Organisation (CSTO) but they regularly clash.
The two sides agreed to a ceasefire on Friday but have since accused each other of breaching it.
After more clashes on Saturday, the night passed "quietly, without incidents" the Kyrgyz authorities said on Sunday morning.
"The country's leadership is taking all measures to stabilise the situation, prevent attempts of escalation... in a peaceful way," they added.
On Sunday afternoon, the Kyrgyz authorities issued a statement saying the situation at the border "remains calm, trending towards stabilisation".
On Saturday, United Nations Secretary-General Antonio Guterres called on the leadership of both sides "to engage in dialogue for a lasting ceasefire, said a spokesman.
Border disputes have dogged the former Soviet republics through their three decades of independence. Around half their 970-kilometre (600-mile) border is still to be demarcated.
In 2021, unprecedented clashes between the two sides killed at least 50 people and raised fears of a wider conflict.