The US has warned Houthi rebels that the peace plan for Yemen that was negotiated with Saudi Arabia and handed to the UN peace envoy will fail if attacks on merchant shipping off the coast of Yemen continue.

The French defence ministry said on Tuesday that the French frigate Languedoc intercepted and destroyed a drone that was threatening the Norwegian oil tanker Strinda in a complex aerial attack originating from Yemen on Monday evening.

The attack caused a fire onboard the tanker, which was sailing under the Norwegian flag, the ministry said.

The Houthis on Tuesday claimed responsibility for the attack on the ship, which was travelling from Malaysia to India. No casualties have been reported.

It is believed two missiles were fired, one from Hodeidah port and another from Huban, east of Taiz.

In solidarity with Palestinians under attack from Israel in Gaza, the Houthis are using their control of Yemen’s western seaboard including ports such as Hodeidah to mount attacks on what it regards as shipping linked to Israel.

The US is hurriedly trying to organise a larger maritime protection force based out of Bahrain to prevent the world’s busiest shipping lanes becoming blocked, and thus crippling the global economy.

Tim Lenderking, the US special envoy for Yemen, who has recently travelled to Doha to hold talks with members of the UN-recognised government, has been consulting Saudi Arabia and Washington on the west’s response. There is pressure in Congress to designate the Iranian-backed Houthis – who have been embroiled in years of civil war in Yemen with Saudi-backed forces – as a foreign terrorist organisation.

Designation would stall the start of the first phase of a three-phase peace plan that has been negotiated between Saudi Arabia and the Houthis, diplomats have said.

If the Houthis were designated a terrorist group, diplomats say, money that was due to be put into banks for the payment of civil servant salaries, a key Houthi demand for the first phase of the peace plan, would be blocked. Similarly the planned opening of any seaports or airports would not be be possible, so keeping the Yemen economy in ruins.

US diplomats are clearly hoping that warnings to the Houthis that they are recklessly and dangerously jeopardising the painstakingly negotiated chance to end Yemen’s nine-year civil war will persuade the group’s fighters to desist from the attacks on maritime shipping.

The warning to the Houthis shows the price the US is willing to pay to support Israel’s plan to eradicate the Hamas leadership.

The US and Saudi Arabia are eager for the Yemeni civil war to end, and believe a basis for doing so was reached in Riyadh that could satisfy the major parties, including the Southern Transitional Council, which is backed by the United Arab Emirates, which wants to see a restoration of the separation between north and south Yemen.

Details of the peace plan that has been handed to the UN envoy for Yemen, Hans Grundberg, have been kept under wraps. It is expected that if all sides agree to its broad principles, including a phased withdrawal of foreign forces, a formal signing ceremony would be held attended by the parties and witnessed by foreign powers.

There has been an unstated truce in Yemen for nearly two years between the Houthis and the Provisional Leadership Council, a coalition of parties opposed to the group.

Western officials say there is no hidden agenda to scupper the three-stage peace plan, just a recognition that it may be politically impossible to stem the growing demands in the US Senate to designate the Houthis as terrorists as these attacks continue.

The US is clear that the Houthis are being given material and political support by Iran, even though individual operational decisions are made independently.

The US secretary of state, Antony Blinken, also spoke to the Chinese foreign minister last Thursday to urge him to join the multinational taskforce to protect shipping in the Red Sea and especially the Bab-el-Mandeb. Blinken argues that China, with its belief in the freedom of navigation and dependence on the Red Sea for its own maritime trade, ought to provide either crew or a ship to the multinational protection force. It would represent a rare example of Chinese US naval cooperation.

Last week the Houthi military commanders extended their legitimate targets from ships with owners linked to Israel to any ships going to and from Israeli ports.

The Houthis are unabashed about their attacks, and their commanders staged a dance on the deck of the Galaxy Leader, the first Israeli-linked ship that it boarded in a daring helicopter raid. The crew of the Galaxy Leader, and the ship itself, remain impounded in Hodeidah port. Cruise missiles have also been fired towards Israel from Yemen, one of which was intercepted by Saudi Arabia, in a rare show of solidarity between the two countries.