The Iran-backed Houthis reportedly advanced to Yemen's strategic Perim Island on Friday, delivering a major boost to the militant group's push to take control of one of the world's most important shipping choke points.

The capture of Perim Island, which was reported by several news agencies, citing multiple Yemeni government sources, comes just one day after the Houthis seized Yemen's port city of Mokha on the Red Sea coast. CNBC could not independently confirm the report.

The rapid ground offensive is seen as a severe setback to Saudi Arabia and the Yemeni forces it backs and puts Iran and its proxies on course to exercise control over two critically important oil choke points on either side of the Arabian Peninsula: the Bab el-Mandeb Strait and the Strait of Hormuz.

Perim Island is a small and rocky area of land that divides the Bab el-Mandeb Strait, a waterway that connects the Red Sea to the Gulf of Aden and to global markets.

There are concerns that the Houthis advance toward the Bab el-Mandeb Strait could have significant ramifications for global trade, particularly if the militant group ratchets up threats or attacks on Red Sea shipping.

Indeed, the capture of Mokha marked a "major blow" to Saudi Arabia as it raises the possibility of the group exerting a tighter grip on the Bab el-Mandeb Strait, according to Hamish Kinnear, principal Middle East and North Africa analyst at risk intelligence company Verisk Maplecroft.

Yemen's port city of Mokha is situated about 75 kilometers (46 miles) north of the Bab el-Mandeb Strait.

"The Houthis were already threatening Saudi shipping from previous positions, but their capture of Mocha opens up the possibility of further advances towards the Bab el-Mandeb coastline and a tighter grip on the chokepoint," Kinnear said in a research note.

As the war continues, Kinnear said both Tehran and Washington believe time is on their side, making a new truce unlikely for now.

"Oil and gas prices, and more specifically refined products such as diesel, will continue to tick upwards while that remains the case โ€“ even if US convoys and Strait of Hormuz export alternatives cushion the price impact," Kinnear said.

The strategic importance of the Bab el-Mandeb Strait has grown significantly since the start of the U.S. and Israel's war against Iran in late February, with the waterway emerging as an alternative route for crude moving toward Asia.

What next for oil prices?

Oil prices traded sharply lower on Friday, but both major benchmarks could still end the week above $100 per barrel for the first time since mid-May.

International benchmark Brent crude futures with November expiry traded 3.3% lower at $104.21 per barrel, while U.S. West Texas Intermediate futures with October expiry were last seen 3.4% lower at $99.08.

The resilience of the oil market is being tested by a clearer recognition of the mounting threat to regional supply, strategists at ING said, with energy market participants seen repricing both the duration and severity of the conflict.

Even as flows continue through the Strait of Hormuz, ING's strategists said flows remain well below prewar levels, underlining how fragile the situation has become.

"Saudi energy infrastructure and crude oil exports from the Red Sea are increasingly at risk, with the Houthis in Yemen targeting Saudi Arabia," ING's Warren Patterson and Ewa Manthey said in a research note published Friday.

"As the Houthis have taken control of the Red Sea port of Mokha in Yemen, recent events increase the threat to shipping around the Bab al-Mandeb Strait," they added.