By Humeyra Pamuk

KINGSTON (Reuters) - U.S. Secretary of State Mike Pompeo, on a visit to Jamaica on Wednesday, cautioned nations against taking "easy money" from China, warning it could be counterproductive, in a second attack in as many days against China's economic role in the region.

Pompeo has been a vocal critic of Chinese investments across the globe that the United States terms "debt diplomacy," alleging that it leaves poorer nations saddled with too much debt.

On a final stop of his Western Hemisphere tour, Pompeo questioned what value Chinese money brings if it "feeds corruption and undermines your rule of law."

"Look into those investments if in fact they ruin your environment, and don't create jobs for your people," Pompeo added.

On Tuesday, he drew the ire of Chinese officials when he said "flashy" Chinese economic promises often produces debt dependency and erode the sovereignty of borrower nations.

China's embassy in Costa Rica responded in a statement that Pompeo spoke "irresponsibly" during his remarks in Costa Rica, saying his assertions were "arbitrary and without grounds."

While in Kingston, Pompeo also doubled down on his criticism of Venezuela's government, telling Caribbean nations that they should look to boost ties with Washington instead.

The days when Venezuela could use its petrodollars to win over neighbors are over, Pompeo said.

He predicted that Venezuela's oil program in the Caribbean, launched in 2005 and known as Petrocaribe, was "fading into the sunset" along with President Nicolas Maduro's administration.

Pompeo's remarks came after Venezuelan state oil company PDVSA announced in a statement that Maduro was "committed to relaunching Petrocaribe with force."

(Reporting by Humeyra Pamuk; writing by Drazen Jorgic; Editing by Jonathan Oatis)