A mass of Iranian pilgrims heading to Iraq for religious rites broke down fences and injured border guards in a stampede, the interior ministry said on Monday, blaming Tehran.

Iranian officials said measures were taken to control the flow of pilgrims at the border while the security forces said they foiled two suicide attacks in Baghdad against the Shiite pilgrims.

The Zurbattiyah border point has seen heavy traffic as the pilgrims cross from Iran to take part in mourning rituals for Imam Hussein, the grandson of the Prophet Mohammed, who is buried in Iraq.

On Sunday, it was discovered that tens of thousands of people attempting to cross had not obtained visas, causing confusion, crowding and a stampede, the ministry said in a statement.

This led to the "smashing of the gates and fences and caused property losses and injured some of the border guards", it said.

"We hold the Iranian side responsible," the ministry said, adding that the breach of the border was meant "to put pressure on the crossing officials to open the border illegally".

A fence was broken by a crowd of pilgrims at the same crossing last year.

"Two million Iranian pilgrims have already entered Iraq," Iran's ambassador to Iraq, Hassan Danifar, told Iranian television Monday.

"We have asked for the flow of pilgrims to be slowed" on the Iranian side, he said.

Iran's official IRNA news agency said some roads leading to Iraq had been closed to pilgrims.

Millions of people take part in Arbaeen commemorations each year. Huge numbers walk to the shrine city of Karbala, leading to the closure of major roads in Baghdad and elsewhere in the country.

The rituals will culminate on Thursday, 40 days after the anniversary of the death of Imam Hussein, who was killed at Karbala in 680 AD.

What is sometimes described as the biggest annual religious gathering in the world is a security headache for Iraq, which is still battling the Islamic State jihadist group on several fronts.

Tens of thousands of security forces are mobilised for weeks across the country to enable the pilgrims to walk to Karbala.

On Monday, security officials said two suicide attacks targeting Shiite faithful marching down the road in Baghdad were foiled.

"A would-be suicide bomber stepped out of a car and towards the pilgrims but a federal police officer shot him dead" before he could set off his explosives, Baghdad Operations Command spokesman Saad Maan said.

The thwarted attack took place in the southern neighbourhood of Saidiyah. Another attack was prevented in similar circumstances in the Shaab district, he said.