According to the state-run Sudan News Agency (Suna) on Monday, Khartoum's UN ambassador al-Fatih Irwa said Foreign Minister Mustafa Osman Ismail would hand Secretary-General Kofi Annan a written complaint.
Irwa added that it decried "the Eritrean regime and its irresponsible practices aimed at destabilising Sudan and undermining the peace process".
Rebels launched an offensive in eastern Sudan's Red Sea State last week in an operation Khartoum said was carried out with the complicity of neighbouring Eritrea.
Officials in Asmara have denied the charges.
Suna added that Ismail would also meet members of the UN Security Council on Monday for talks that would also cover the January peace accord that ended 21 years of war in Sudan between the north and the south and the government's reconciliation deal with the opposition.
Rebels in eastern Sudan accused the government at the weekend of launching an intensive aerial bombing campaign on civilian targets in the Red Sea State in retaliation for losing ground battles against the opposition Eastern Front.
The eastern rebels, who launched an offensive near the country's main Port Sudan, have accused Khartoum of pursuing a policy similar to that used in Sudan's troubled western Darfur region.
Both the eastern and western groups say their regions are being marginalised by the Arab-dominated government in Khartoum.
Meanwhile, a government committee completed the drafting of a constitution for a six-year interim period provided for in a January peace deal that ended two decades of war between north and south.
The document, which was presented to President Omar al-Beshir, is due to be approved by parliament and the autonomous government of South Sudan before the beginning of the interim period, scheduled for 9 July.
Rebels from Sudan's Eastern Front
decry Khartoum's use of airpower
At a ceremony in Khartoum's Republican Palace, al-Beshir hailed the fact that the National Constitutional Revision Commission (NCRC) unanimously agreed on the new basic law.
"The passage of the draft constitution unanimously without the need for vote-taking among the NCRC transmits a message to the world that the Sudanese people are tolerant and are capable of putting past grievances behind, however severe they were," he said.
The 60-member NCRC includes a majority of representatives from the ruling National Congress and a little less than a third of former southern rebels from John Garang's Sudan People's Liberation Movement, with whom al-Beshir's government signed a peace agreement in Kenya in January.
The rest of the seats were given to opposition members, including from the National Democratic Alliance, which ended a 16-year feud with al-Beshir's government by signing a reconciliation deal in Cairo last week.
The six-year interim period which is due to kick off with an official ceremony in Khartoum on 9 July will lead to a referendum on self-determination for the South.
The January peace deal ended a 21-year conflict that left an estimated 1.5 million people dead and displaced another four million.