Hague, commenting Tuesday in London, praised the European Union's decision to proceed with a ban on Iranian oil starting Sunday and warned more punitive actions from Western nations could be forthcoming.
The comments came following "frank but difficult" negotiations between Iran and the E3+3 nations -- France, Germany, Britain, China, Russia, and the United States -- in Istanbul, Moscow and Baghdad that produced little headway.
The two sides have agreed to have follow-up, technical level meeting Tuesday in Istanbul.
The EU Foreign Affairs Council announced the latest package of sanctions Monday in Luxembourg.
Hague asserted Iranian negotiators have so far "failed to agree any concrete steps to address the international community's serious concerns" about the country's suspected nuclear weapons program.
"The U.K. government will argue for intensified sanctions over the coming months if there is no progress made in these negotiations," Hague said, adding, "it is not too late for Iran to give a more promising response to the offer of the E3+3, but they have not yet done so."
The sanctions called for import contracts on Iranian oil to be terminated by Sunday and for EU insurers to stop providing third-party liability and environmental liability insurance for the transport of Iranian oil.
The new measures "reflect the international community's resolve and our determination, to intensify the peaceful pressure on Iran until it starts to build confidence that its nuclear program is purely peaceful," Hague said.
First approved in January, the measures outlaw the export of key oil sector equipment and technology to Iran as well as new investments in Iranian petrochemical companies.
Trade with Iran's public bodies and central bank in gold, precious metals and diamonds is banned as well.
Iran insists its nuclear enrichment activities are meant solely for civilian and industrial uses, as permitted under international treaties, and argues the International Atomic Energy Agency has failed to turn up any evidence of diversion of nuclear materials toward military uses despite frequent inspections.
Iranian Foreign Minister Ali Akbar Salehi suggested Tuesday that Europe should reconsider the oil embargo and "adopt more rationality in dealing with Iran," the official Islamic Republic News Agency reported.
Speaking in Cyprus -- which assumes the rotating EU presidency Sunday -- Salehi said, "We got used to sanctions as they are not new to us but we hope the European Union will review its unilateral sanctions with more rationality," adding, "confrontation will be to no one's benefit."
Citing its "special status in the Middle East," Salehi said he expected Cyprus to act as a bridge between Iran and the European Union during its presidency.
Celebrity Couples of 2014 [PHOTOS]