"Eritrea is not willing to negotiate or be part of the regional peace process," he said.
Djibouti and neighboring Eritrea have engaged in two border conflicts. In 1996, they almost went to war after a Djiboutian official accused Eritrea of shelling the town of Ras Doumeira.
Three years later, in 1999, Eritrea accused Djibouti of siding with longstanding rival Ethiopia, while Djibouti counter-accused Eritrea of supporting rebels fighting its government.
As a result, Djibouti recalled its ambassador and broke off relations with Eritrea, which weren't restored again until 2001.
The two countries clashed again for three days in the summer of 2008, leading to a further deterioration of ties and a U.N. embargo on Eritrea.
Since 2010, Qatar has played the role of mediator between the two antagonists.
Under Qatari mediation, Djibouti has released hundreds of Eritrean prisoners, who were handed over to the United Nations. Eritrea, however, has yet to follow suit.
"Djibouti has already handed over Eritrean prisoners of war (POWs) seized during the 2008 border conflict," Youssouf said. "However, we have no information about Djiboutian POWs."
"We are sad that there is no willingness on the Eritrean government's side towards peace," he said. "Qatar is running after Djiboutian POWs; however, there has been no change – and the same goes [for arbitration] between Ethiopia and Eritrea."
"We want Eritrea back to IGAD [the Intergovernmental Authority on Development, an East African regional bloc based in Djibouti], but the leadership in Eritrea is not helping itself," Youssouf asserted.
Djibouti's top diplomat also stressed his country's good relations with Addis Ababa.
"We are working to facilitate Ethiopian development through the expansion of infrastructure and improved port service delivery, so as to satisfy the country's import and export needs," he said.
"Our partnership [with Ethiopia] is based on mutual respect and understanding," Youssouf said, adding that Djibouti and Ethiopia should be considered the "engines" of the Horn of Africa region.
"Ethiopia and Djibouti can be considered engines to the region, as they are strengthening their relations day by day," he asserted. "Our integrity will be a model for other countries."
As for war-torn Somalia, Youssouf said Djibouti had deployed 1,000 peacekeepers to the long-troubled state and was ready to send another 1,000 if necessary.
"We need peace in Somalia because Djibouti will not be peaceful if there is no peace in Somalia," he said. "Hence, we will not evacuate from Somalia until that country manages to stand on its own."
Somalia has remained in the grip of on-again, off-again violence since the outbreak of civil war in 1991.
Earlier this year, the country appeared to inch closer to stability after government troops and African Union forces – deployed in the country since 2007 – drove the Al-Qaeda-linked Al-Shabaab group from most of its strongholds.
"Being home to IGAD, Djibouti feels a special responsibility for peace in the region as a whole," Youssouf said.
He went on to note that IGAD had helped Somalia form a government and was currently helping resolve the conflict between Sudan and South Sudan.
"Since the start of the crisis in South Sudan a year ago, IGAD leaders have held five meetings to find a solution to the crisis," he said. "A recommendation has already been put in place; we expect there will be a solution."
In recent months, IGAD has sponsored peace talks between South Sudan's President Salva Kiir and rebel leader Riek Machar. The country fell into violence and chaos last year when Kiir accused Machar of trying to overthrow his government.
Youssouf said Djibouti was fighting terrorism in cooperation with the international community.
"As a result, the terrorist Al-Shabaab group is being defeated… and driven out of Somalia," he said.
"We are involved not only in stabilizing Somalia, but also in peacekeeping activities in Cote d'Ivoire, the Central African Republic and South Sudan, among others," he added.
Turning to Yemen's political turmoil, the foreign minister accused "external hands" of sowing strife in the poor Arab country.
"We need global cooperation [to maintain] the security of the Red Sea, as the matter is global," he said, going on to stress that Djibouti, Ethiopia and Yemen all enjoyed good relations.
"They [the three countries] do their level best for the security of the Red Sea, but Eritrea is not cooperating," he said. "Djibouti continues to host naval forces so we can prevent piracy."
As for relations with Turkey, the Djiboutian minister said Ankara enjoyed "special" ties with all Horn of Africa states.
"We appreciate Turkish support for Somalia and the Horn [of Africa] countries as a whole," he said. "Turkey is a significant partner to Africa."
Youssouf went on to note that Turkish President Recep Tayyip Erdogan had been the first foreign leader to visit Somali capital Mogadishu when he still served as Turkish prime minister.
Chamber of Commerce complaint regarding containers at Port
In other news, the Djiboutian Chamber of Commerce has complained that the accumulation of Ethiopian containers was causing congestion at the Port of Djibouti, the country's principal outlet for maritime trade with neighboring Ethiopia.
"Ethiopian containers that have accumulated at the port are causing congestion," chamber chairman Youssouf Moussa Dawaleh told reporters on Friday.
"Some of the containers have been stuck at the port for more than two years now," he said.
Ethiopian Ambassador to Djibouti Suleiman Dedefo, for his part, said that containers were backed up due to "capacity limitations" on the part of Ethiopian importers. Dedefo noted that the port typically saw container congestion each year during the period from August to December.
"This is when we import fertilizers; the same happens when we import wheat or sugar, he said.
The ambassador added: "Establishing good transport companies and upgrading infrastructure would help solve the problem."