Saudi Arabia's Crown Prince Mohammed bin Salman has accused Iran of an act of "direct military aggression" by supplying missiles to rebels in Yemen.
This "may be considered an act of war", state media quoted the prince as telling UK Foreign Secretary Boris Johnson in a telephone conversation.
On Saturday, a ballistic missile was intercepted near the Saudi capital.
Iran has denied arming the Houthi movement, which is fighting a Saudi-led coalition backing Yemen's government.
Foreign Minister Mohammad Javad Zarif said on Monday that Saudi Arabia's "wars of aggression" and "regional bullying" were threatening the Middle East.
Houthi-aligned media reported that the rebels had fired a Burkan H2 ballistic missile at King Khaled International Airport, which is about 850km (530 miles) from the Yemeni border and 11km north-east of Riyadh, on Saturday evening.
Saudi media reported that missile defences intercepted the missile in flight, but that some missile fragments fell inside the airport area. No casualties were reported.
Human Rights Watch said the launch of an indiscriminate missile at a predominantly civilian airport was an apparent war crime.
The official Saudi Press Agency reported on Tuesday that in his telephone call with Prince Mohammed, Mr Johnson had "expressed his condemnation of launching a ballistic missile by Houthi coup militias" and affirmed "Britain's stand with the kingdom of Saudi Arabia in confronting security threats".
"For his part, the crown prince stressed that the involvement of the Iranian regime in supplying its Houthi militias with missiles is considered a direct military aggression by the Iranian regime and may be considered an act of war against the kingdom," it added.
Saudi Foreign Minister Adel al-Jubeir told CNN on Monday that Lebanon's Hezbollah movement, an Iranian proxy, was also involved.
"It was an Iranian missile launched by Hezbollah from territory occupied by the Houthis in Yemen," he said.
Regional 'Cold War'
By Jonathan Marcus, BBC diplomatic correspondent
Iran and Saudi Arabia are engaged in a regional "Cold War"; a battle for influence and power. And just like the US-Soviet Cold War, while the two main protagonists are not directly involved in fighting each other, they or their proxies are engaged on a number of other battlefields.
The Saudis went into Yemen to counter alleged Iranian influence, but the campaign has proved a quagmire for the Saudi forces.
Iran is in the ascendant in Iraq, where it is a close ally of the Shia-dominated government. And it is "winning" in Syria too, helping to stabilise and consolidate the Assad regime. Saudi support for Syrian rebel factions has achieved nothing.
Now the Saudis seem to be focusing on another country where Iran's allies - in this case, Hezbollah - are well entrenched - Lebanon. But tinkering with that country's fragile stability has huge risks - not least the danger of prompting a crisis that could lead to a full-scale war between Israel and Hezbollah.
He added that the missile was similar to one launched in July that was shot down close to the Saudi city of Mecca, and that it was manufactured in Iran, disassembled and smuggled into Yemen, then reassembled by "operatives from the Iranian Revolutionary Guards and Hezbollah".
Mr Jubeir warned that "Iranian interventions in the region are detrimental to the security of neighbouring countries and affect international peace and security".
His Iranian counterpart dismissed the allegation in a series of tweets.
"KSA bombs Yemen to smithereens, killing 1000s of innocents including babies, spreads cholera and famine, but of course blames Iran," Mr Zarif wrote.
An Iranian foreign ministry spokesman earlier said that the missile launch was "an independent action" in response to Saudi-led coalition "aggression" and that Iran had nothing to do with it.
In response to the attack, the coalition announced the "temporary" closure of all Yemeni land, sea and air ports, but said humanitarian aid could continue to enter Yemen under strict vetting procedures.
But the United Nations said it was prevented from sending two aid flights on Monday.
More than 8,670 people - 60% of them civilians - have been killed and 49,960 injured in air strikes and fighting on the ground since the coalition intervened in Yemen's civil war in March 2015, according to the UN.
The conflict has also left 20.7 million people in need of humanitarian assistance, created the world's largest food security emergency, and led to a cholera outbreak that is believed to have affected 902,000 people and caused 2,191 deaths.