Abdullah escaped an assassination attempt yesterday when two blasts hit his campaign motorcade in Kabul, killing at least six people just ahead of next week's hotly contested runoff.
"The members of the Security Council underlined their support for Afghanistan's democratic processes, and looked forward to the second round of the presidential election and the continued orderly transition to a new administration," they said in a statement.
They condemned terrorist attacks against civilians and "attempts to disrupt elections by targeting election personnel, candidates or infrastructure."
The council members also expressed their sympathy and condolences to the families of the victims, and to the people and government.
It was the second attack targeting Abdullah during Afghanistan's election season, which has seen an uptick in violence with the Taliban threatening to disrupt the polls.