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Speaking to CNBC's "Squawk Box," Bessent added, "How do we do that? That if they land, you cannot provide them with fuel. You cannot provide them with landing services, you cannot sell them tickets, or you will be knocked out of the dollar system."

The Treasury Secretary said that Washington was pressuring Iran "like never before," saying that the U.S. was putting a stop to Iran's enablers around the world, such as sanctioning banks.

Last week, the Treasury announced new sanctions on Russia's state-controlled VTB Bank as part of its effort to economically isolate Iran by targeting its business partners and other financial "enablers."

G7 condemns Houthi strikes

Separately, the G7 group of nations have called for an end to attacks by Iranian-backed Houthi rebels against Yemen and Saudi Arabia on Monday stateside, condemning the "unacceptable continued strikes" by the group.

The bloc also called on the Houthis to cease all military actions, attacks against civilian shipping and for Iran to end its support for the rebel group.

The Houthis reportedly said they attacked "sensitive" sites in the Saudi capital Riyadh on the weekend, with fire and smoke seen near the city's airport.

Houthi rebels also recently seized Yemen's Perim Island on the Red Sea, tightening their grip on the Bab el-Mandeb Strait, which puts Iran and its proxies on course to exercise control over two critically important oil choke points: that and the Strait of Hormuz.

The Bab el-Mandeb Strait is an important alternative for oil exports to bypass the Strait of Hormuz, especially for Saudi Arabia, whose East-West pipeline allows the kingdom to divert some oil flows to be exported from the Red Sea.

Topographic map showing the Middle East region and Arabian Peninsula with focus on critical maritime chokepoints for international commerce. The Strait of Hormuz is marked in the northeast, connecting the Persian Gulf to the Gulf of Oman. Bab-al-Mandeb Strait is highlighted in the southwest, linking the Gulf of Aden to the Red Sea.

Rbkomar | Moment | Getty Images

The G7 statement comes after the U.K. reportedly said it will support Saudi Arabia against Iranian backed Houthi rebels, with the Royal Air Force providing air to air refueling of Saudi planes.

Prime Minister Andy Burnham told reporters that the arrangement will be for a matter of weeks, and will be kept under review.

The move comes as U.S. President Donald Trump refused Riyadh's request for help against the rebels on the weekend, reportedly cancelling a planned airstrike.

Burnham said he was "acting to secure the interests of Britain and the wider region, because of course Saudi Arabia has been experiencing attack, is looking at potential further disruption, and we need to keep those pathways (for oil) open," according to the Associated Press.

Last week, NATO Secretary Mark Rutte signaled that European nations could also provide support to Saudi Arabia, telling a BBC interview that "I would not be surprised if some phone calls were taking place between European allies — 'hey, how are we going to deal with this?'"