After a series of meetings with US officials in Washington, Ismail told Aljazeera that Sudan could no longer remain silent towards Eritrea's support of an armed rebellion in the east of Sudan, bordering Eritrea.
Speaking to Aljazeera by telephone from the Eritrean capital, Asmara, Eritrea's Assistant Foreign Minister Muhammad Umar Mahmud denied the charges.
"I found Ismail's announcements strange as they come at a time when Sudan is heading to a new stage, where a new government of national unity is about to be formed in accordance with the Nivasha and Cairo agreements," he said.
"Thus, Sudan's foreign minister is talking on behalf of the current government, which will no longer be in power in less than two weeks."
Mahmud brushed off the foreign minister's accusations by saying such "irresponsible" announcements have been made by Ismail for the past three years.
"This threat does not frighten us," he added.
When asked about Sudan's accusation that Eritrea supports an armed rebellion in eastern Sudan, Mahmud said: "This is untrue as Sudan has already accused us of supporting the Sudan People's Liberation Movement (SPLM) whose head, Dr George Garang, will be the first vice-president in the government of national unity, Sudan's new government, within two weeks.
"Garang and the Democratic National Alliance, which signed an agreement with Khartoum in Cairo on 18 May, met in Asmara three days ago," he added.
"This threat does not frighten us"
Muhammad Umar Mahmud,
Eritrean Assistant Foreign Minister
They will hold a meeting in Asmara next Monday. Then, they will move to Khartoum.
Mahmud said: "We do not support any group and they know this very well because they not only recognise these armed groups but hold talks with them in Abuja and other places."
Mahmud also said they welcomed the coming era and looked forward to normalising ties with Khartoum.
"We look forward to healthy and normal relations between the two countries, especially since half of the new government of national unity will have Eritrea-friendly members," he told Aljazeera.
"We are not excluding the rest of the members of the Sudanese government with whom we have good relations as well," he added.
He affirmed Eritrea's efforts in supporting and ensuring the unity of the Sudan and its people.
"We are ready to cooperate with the coming government of national unity and to open a new chapter," he added.