NEW YORK — In a dramatic escalation of American pressure over the ongoing European refusal to designate Hezbollah a terror organization, the US Senate will consider in the coming days a resolution urging European governments and the European Union to make the designation and impose sanctions on the organization.

The goal, the resolution explains, is to prevent Hezbollah from using the territory of the European Union “for fundraising, recruitment, financing, logistical support, training, and propaganda.”

Drafted by outgoing Connecticut Sen. Joe Lieberman and already co-signed by over 50 senators, the resolution calls on US President Barack Obama to “provide information about Hezbollah to the European allies of the United States and to support to the Government of Bulgaria in investigating the July 18, 2012, terrorist attack in Burgas,” an attack believed by the Israeli and US governments to be the handiwork of the Lebanese group.

The resolution is the latest in a series of calls from the US government for European governments and the EU to rethink their refusal, which many European leaders believe will harm their relations with the Lebanese government in which Hezbollah is a coalition partner.

In a conference call with journalists on August 10, US Under Secretary of the Treasury for Terrorism and Financial Intelligence David Cohen noted that “before al Qaeda’s attack on the US on September 11, 2001, Hezbollah was responsible for killing more Americans in terrorist attacks than any other terrorist group.”

On October 26, John Brennan, Obama’s top counterterrorism advisor, told a think tank in Ireland that “failure to designate Hezbollah as a terrorist organization makes it harder to defend our countries and protect our citizens. As a result, for example, countries that have arrested Hezbollah suspects for plotting in Europe have been unable to prosecute them on terrorism charges.”

Speaking at the Institute of International and European Affairs in Dublin, he insisted that the organization’s ‘‘social and political activities” — frequently cited by European governments in explaining their refusal — “must not obscure [the group’s] true nature or prevent us from seeing it for what it is — an international terrorist organization actively supported by Iran’s Islamic Revolutionary Guards Corps-Quds Force.”

Quoting Cohen and Brennan, the Senate resolution notes that Hezbollah “continues to receive training, weapons, and explosives, as well as political, diplomatic, monetary, and organizational aid, from Iran.”

The resolution offers a litany of anti-American terror attacks in which Hezbollah has been implicated over the last three decades, “including the bombings in Lebanon in 1983 of the United States Embassy, the United States Marine barracks, and the French Army barracks, the airline hijackings and the kidnapping of European, American, and other Western hostages in the 1980s and 1990s, and support of the Khobar Towers attack in Saudi Arabia that killed 19 Americans in 1996.”

Hezbollah was also involved in training Shiite insurgents in Iraq that targeted US troops, the resolution notes, and in the 1992 and 1994 attacks in Buenos Aires, Argentina, the former targeting the Israeli embassy and the latter the city’s AMIA Jewish community center.