The central government in Baghdad has cracked down hard on the Kurds since the government of the Kurdish autonomous region staged an independence referendum on Sept. 25 that Baghdad considers illegal.
The Iraqi armed forces have threatened to resume military operations against the Kurds, accusing them of delaying the handover of control of borders and taking advantage of negotiations to bolster their defences.
"We will regain control on border areas without escalation. But our patience will run out. We will not wait forever. We will take action," Abadi said at a news conference.
The independence vote defied the central government in Baghdad -- which had ruled the ballot illegal -- as well as neighbouring Turkey and Iran which have their own Kurdish minorities.
Abadi spoke a few hours after the Kurdistan Regional Government (KRG) announced a concession to Iraq's central government by saying it would accept a court decision prohibiting the region from seceding.
The announcement marks the Kurds' latest attempt to revive negotiations with Baghdad over their region's future after the central government imposed measures in retaliation against the independence vote.
Among the steps was an offensive by Iraqi government forces and the Iran-backed Popular Mobilisation Forces that took back the oil city of Kirkuk and other disputed territories from the control from the Kurdistan Regional Government (KRG) last month.
The KRG said on Tuesday it would respect the Nov. 6 ruling by the Supreme Federal Court, which declared that no Iraqi province could secede.
"We believe that this decision must become a basis for starting an inclusive national dialogue between (Kurdish authorities in) Erbil and Baghdad to resolve all disputes," the KRG said in a statement.
Abadi had previously urged the northern semi-autonomous Kurdish region to abide by the court's decision.
The court is responsible for settling disputes between Iraq’s central government and the country's regions and provinces. Its decisions cannot be appealed, though it has no mechanism to enforce its ruling in the Kurdish region.