Relations have been tense since the Horn of Africa nations engaged in a three-day conflict in 2008.
“Qatari peacekeepers withdrew on June 12 and 13. On the same day, there were Eritrean military movements on the mountain,” Ali Youssouf told the Reuters news agency.
“They are now in full control of Dumeira Mountain and Dumeira Island. This is in breach of the UN Security Council resolution,” he added, referring to areas that the neighbours dispute.
Authorities in Eritrea were not immediately available for comment.
Qatar’s foreign ministry did not give a reason for the move.
On June 5, a Saudi-led bloc of countries announced they were cutting ties with Qatar, accusing it of supporting “terrorists” – allegations Doha strongly denies.
Djibouti, a close Western ally, hosts French and US military bases and is the main route to the sea for Eritrea’s arch foe and Washington’s top regional ally, Ethiopia.
Eritrea has fractious ties with the West, which had previously accused it of backing Somali and other regional armed groups. Asmara denies the charges.
According to Abdullahi Boru Halakh, a Horn of Africa analyst, the territorial dispute at the border “has always been there, but for the past years Qatari forces that had been deployed there had kept peace”.
Speaking from the Kenyan capital, Nairobi, he argued that Eritrea is trying to take advantage of the Gulf crisis.
“Eritrea is in the cold and under UN sanctions,” he told Al Jazeera.
“They also have a territorial dispute with Ethiopia which has been simmering for years. The UN ruled in favour of Eritrea, but the ruling has not been enforced. Eritrea now sees this as an opportunity to come back from the cold and maybe get aid from the UN which it desperately needs.”
Clashes broke out between the Horn of Africa countries in June, 2008, after Djibouti accused Eritrea of moving troops across the border, raising fears the spat could engulf the entire region.
The dispute triggered several days of fighting that killed a dozen Djiboutian troops and wounded dozens.
Eritrea had initially denied making any incursions, accusing Djibouti of launching unprovoked attacks.
The UN Security Council then requested both sides withdraw from the area, before the neighbours accepted a Qatari request to mediate and deploy peacekeepers.