Venezuela's opposition leader Juan Guaido has met with US Secretary of State Mike Pompeo in Colombia's capital, as he tries to shore up international support amid a power struggle with President Nicolas Maduro.

The South American country, which is suffering an economic crisis, is a "failed state", Pompeo said on Monday, after meeting Guaido on the sidelines of a three-day counterterrorism ministerial meeting in Bogota.

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Guaido, recognised as the nation's legitimate president by more than 50 countries, including the United States, defied a court order to travel abroad on Sunday.

"We are honoured by your presence," Colombian President Ivan Duque told the opposition leader on Monday during opening remarks. "You will always have a friend in Colombia."

Duque also met Pompeo before the start of the ministerial meeting to discuss a number of issues, including the situation in Venezuela.

"I would fully expect there will be further action that the US would take to continue to support President Guaido and the Venezuelan people," Pompeo told journalists.

"We do not talk about particular sanctions but everyone can fully expect that the US is not done," Pompeo warned, without specifying what action Washington will take.

From Colombia, Guaido is set to travel on to London, Brussels and Davos, Switzerland, to attend the World Economic Forum.

"We will have important meetings in Europe, in the European Union and specifically in Davos," Guaido told journalists.

Guaido would not confirm whether he will meet US President Donald Trump in Davos.

Meanwhile, Maduro's government, which is backed by Russia and China, among others, dismissed Guaido's trip as "irrelevant".

"It's utterly irrelevant for us that a lackey has gone to meet his masters in Colombia," ruling Socialist Party Vice President Diosdado Cabello told a press conference in Caracas, referring to Guaido.

"He hasn't achieved anything he promised."

Maduro has branded Guaido a US puppet and says the US wants to invade Venezuela using the aid of Colombia and other countries.

According to analyst Carlos Pina, the opposition leader "is playing his last card".

"Currently Maduro and his government seem to be holding most of the [political and military] power in Venezuela," Pina said.

"With this trip, and with not much margin inside the country, what Guaido is trying to do is to increase the international pressure and the support of his [international] allies," he added.

National Liberation Army and Hezbollah

Separately, Colombia and the US accused Maduro of harbouring armed groups such as Colombia's Marxist-led National Liberation Army rebels and of having connections to everyone from drug traffickers to Lebanon's Hezbollah movement.

"[Maduro is] now running an operation that looks more like a cartel than anything else that one could describe. This isn't good for Venezuela, it's not good for the countries that are around Venezuela," Pompeo said.

There was no immediate response by Caracas.

Earlier on Monday, Colombia and Honduras officially declared Lebanon's Hezbollah a "terrorist" organisation, a move praised by Pompeo.

We applaud the announcements of Colombia, Honduras, and Guatemala to designate #Iran-backed #Hizballah a terrorist organization. It and other transnational terrorist groups remain active in the region. The U.S. continues to rally international support to counter these threats. — Secretary Pompeo (@SecPompeo) January 20, 2020

According to Pina, the statements "could open the possibility of the US including Venezuela in the list of states that support or finance terrorism".

He said: "If this were to take place, it would be an unprecedented event that could lead to a big escalation between the different parties."