The missiles fired from Yemen to the Saudi capital, Riyadh, are characteristic of Iran-supplied weapons, the United States Ambassador to the United Nations Nikki Haley said.
Addressing members of the UN Security Council, Haley said the missile "has similarities with missiles in similar attacks using Iranian supply weapons".
"We must act together to uncover the crimes of the Tehran regime and do whatever it takes to ensure they get their message."
"If we do not do it, Iran will bring the world more into the regional conflict," Haley said.
Haley then proposed a series of actions that could be done by the UN Security Council, but Russia, which is allied with Iran, indicated it would not support the action plan.
Previously, Iran insisted on denying arms of Houthi rebels in Yemen.
Al Masirah TV channel belonging to the Houthi rebel group in Yemen says the missile target is a meeting of Saudi Arab leaders at the Al-Yamama Palace, which is the headquarters of the King as well as the royal court.
The missile was aimed at 'Saudi leaders' incident at Al-Yamama Palace in Riyadh' with an agenda among others estimated to be an annual budget discussion and attended by Crown Prince, Mohamed bin Salman, according to Al Masirah.
A few minutes later, a Saudi government TV station reported an intercept was intercepted just south of the capital.
A video - published by a man claiming to be in Olaya district - shows white smoke over Riyadh and an explosive sound is heard.
A spokesman for Saudi-led coalition forces, Turkish Colonel al-Maliki, said the missiles have been denied using Patriot missiles.
He said the attack proved Iran's "continued involvement" in favor of Houthi.
Early last month, a missile was also successfully intercepted before hitting Riyadh airport. These missiles, according to the US ambassador to the UN, Nikki Haley, are clearly made in Iran.
UN data show more than 8,670 people have died and 49,960 have been wounded since coalition troops interfered in the war in Yemen.
The war also caused 20.7 million people to need humanitarian assistance and helped inflict a cholera outbreak that is estimated to have killed 2,219 people since April.