Omar also predicted that with many outstanding issues already resolved, an agreement could be signed a few days after the discussions commence, saying "the final agreement will be signed by the two sides on June 16."
The NDA, a coalition of northern, southern eastern and western opposition groups, including the Sudan Peoples' Liberation Movement (SPLM), confirmed talks with the government would resume on June 11.
"The discussions will start on Saturday," NDA vice president Abdul Rahman Saeed told AFP.
But he did not share the government's optimism that a deal could be signed five days later, saying "it was possible, but not certain."
Saeed explained that the talks will kick off with meetings aimed at reaching a deal on how to implement an initial agreement the two sides signed in January, particularly on political and military issues.
"We have already agreed," he said, adding that the discussions will focus on "implementing what we have agreed upon."
The NDA and Khartoum struck a deal in mid-January that envisaged lifting the state of emergency in place since 1989 and setting up a joint commission to look at how to reintegrate the NDA into Sudan's political life.
It further called for the establishment of a "democratic and pluralist" regime that respects "democratic freedoms and human rights".
A final accord was to be signed on February 12 in the Egyptian capital, but it did not happen.
A three-way meeting bringing together NDA leader Mohammed Osman al-Mirghani, Sudanese first Vice President Ali Osman Taha and SPLM chairman John Garang, will be held on June 15 to iron out lingering differences, said Saeed.
They will also prepare the final text of the agreement and decide on a date for the signing ceremony.
The accord, said Saeed, will not be binding to certain NDA members such as the Darfur-based Sudan Liberation Movement (SLM) and the Eastern Front, comprising the Beja Congress and the Free Lions Movement.
The SLM has a different negotiating forum with Khartoum and the Eastern Front walked out of talks between the NDA and government, also demanding a separate forum for negotiations.