"We agreed to maintain an atmosphere of peace, as was the case during the election.
The SPLM, which dominates politics in the south of the country, on Monday accused the predominantly-northern NCP of preparing to rig the elections in Blue Nile state, which lies on the border between the two halves of the country.
Other parties have also accused the government of irregularities in polling and withdrew from some of the presidential, parliamentary and local ballots in protest before polling took place.
The withdrawals left Bashir almost certain of retaining the presidency and after the first day of counting of the legislative election ballots it became clear that his NCP would dominate parliament
Those early results prompted several opposition parties to accuse the ruling party used state resources to fiddle with ballot boxes over the five-day voting period.
The NCP has rejected the claims.
The United States has also said that the election process was plagued by "serious irregularities
"The United States regrets that Sudan's National Elections Commission did not do more to prevent and address such problems prior to voting," the White House said in a statement.
It said that the US was committed to helping ensure a 2011 referendum on southern independence was conducted fairly.
The NCP and SPLM serve in a power-sharing government that agreed as part of a deal signed in 2005 to end a bloody civil war. Part of that deal also set up next year's vote on whether the south should secede.
At the meeting between Taha and Kiir, the two parties agreed to speed up the implementation of the Comprehensive Peace Agreement, "particularly the issue of border demarcation," Taha said.