He said there had been a report that there would be a ceremony around the main mosque, and the United Nations mission should avoid the area because of traffic. The council called the deteriorating humanitarian situation "dire", saying Yemen "stands at the brink of catastrophic starvation".
Reportedly, clouds of smoke could be seen coming from the building amid the clashes between the Houthi rebels and loyalists of former president Ali Abdullah Saleh.
The Houthi-controlled interior ministry distributed a video of dozens of seated barefoot men it said were pro-Saleh fighters detained in one of its party headquarters.
Tens of thousands of Houthi supporters staged a rally in Sanaa on Tuesday to celebrate what the Houthis had said was the defeat of a major conspiracy by Saleh, chanting slogans against Saudi Arabia and its allies.
But with Saleh's forces seemingly in disarray, it was not immediately clear if the Saudi-led coalition would be able to turn the split to its advantage. They spoke on condition of anonymity, fearing reprisals.
Dujarric, the U.N. spokesman, told reporters that U.N. special envoy for Yemen Ismail Ould Cheikh Ahmed told a closed meeting of the U.N. Security Council that the killing of Saleh and others was "an adverse development" that will "constitute a considerable change to the political dynamics in Yemen".
Much is likely to depend on the future allegiances of Saleh loyalists who previously helped the Houthi group, which hails from the Zaidi branch of Shi'ite Islam that ruled a thousand-year kingdom in northern Yemen until 1962.
Both Saleh forces and the Houthi rebels are battling to capture the capital city. The coalition has imposed a blockade on the country, with the aim of reinstating the internationally recognized government of Saleh's successor, Abed Rabbo Mansour Hadi (HAD'-ee).
The protest took place outside a rebel-run hospital where the body has been kept since he was killed on Monday by his onetime allies, the Iran-backed Shiite rebels known as Houthis.
But over the past year, the Houthis appear to have undermined Saleh, wooing away some of his commanders.
A least 234 people were killed in fighting that the International Committee of the Red Cross described as the fiercest since the start of the conflict.
The fighting has claimed more than 10,000 lives since then.