Al-Maliki has called for a full manual recount and his bloc has submitted legal complaints, but Iraq's election commission dismissed those calls, saying there had been no evidence of serious electoral fraud.
The Security Council congratulated the people and government of Iraq for holding a "successful election" and welcomed Friday's announcement of the provisional results by the Independent High Electoral Commission (IHEC), saying it looked forward to certification by the Iraq's supreme court.
Security Council members noted the findings of international and independent Iraqi observers "who affirmed their confidence in the overall integrity of the election".
"The members of the security council look forward to the formation of the new government in a spirit of co-operation and respect for national unity," it said in a statement.
In Baghdad, both Allawi and al-Maliki are seeking to assemble coalitions to get the 163 seats necessary to secure a majority in parliament and form a government.
Allawi was dealt a blow this week when the Justice and Accountability Commission said six members of his Iraqiya bloc should not have been allowed to stand in the polls.
The commission, charged with preventing former members of Saddam Hussein's banned Baath party from returning to public life, said it would appeal to the IHEC to have the six barred from parliament.
Allawi also complained this week that Tehran was "interfering" in the political process to try to block his path by holding talks with all of Iraq's major political groups except his secular Iraqiya bloc.
Senior figures from al-Maliki's State of Law Alliance and other major Iraqi blocs have visited the Iranian capital since the polls, but no official from Iraqiya is known to have travelled to Tehran.
Iran denied it was meddling in Iraqi politics, with a foreign ministry spokesman telling state radio on Wednesday that efforts by Iraqi parties "to form the next government are an internal matter, and they will obviously do that according to their electoral plans and without taking into account foreign interests".
"Iran does not interfere in this," he said, but added that Tehran was ready to "host Iraqi political movements to help with the formation of the new government as soon as possible".
Whether Allawi or al-Maliki gets to be prime minister could hinge on a referendum planned by the movement led by Muqtada al-Sadr, the Shia Muslim religious leader.
Al-Sadr's movement emerged from the polls as the most powerful faction in the INA bloc that could help form a coalition government and Friday's referendum is to gauge support levels among its supporters for would-be prime ministers, including al-Maliki and Allawi.