“We are committed to go forward in resolving these pending issues with our southern neighbours, through understanding, to reach good relations,” Bashir told the Baghdad gathering, which opened with a call for peace from UN chief Ban Ki-moon.
Bashir noted that Arab leaders had been following events on the southern border.
“The enemies of peace were pushing South Sudan to attack”, he said.
Each side accused the other of starting the fighting which began on Monday.
It was the worst violence since South Sudan declared independence from Khartoum in July last year following an overwhelming vote after Africa’s longest war.
Officials in South Sudan’s Unity state said the border was calm on Thursday, although northern warplanes were reported to be still flying over the state.
The African Union, UN Security Council and European Union have all called for an end to the fighting.
US Secretary of State Hillary Clinton accused Khartoum of bearing most of the responsibility for the renewed hostilities.