LISBON (Reuters) - Portugal's Socialist government has warned crisis-hit Venezuela that bilateral ties could be at risk over its jailing of Portuguese supermarket managers on charges of gouging food prices and demanded that the problem be resolved swiftly.

Portuguese Foreign Minister Augusto Santos Silva said he had "a tough conversation" over the issue with his Venezuelan counterpart Jorge Arreaza in New York on the sidelines of the United Nations General Assembly on Monday.

The brewing diplomatic row could sour relations between Portugal's left-leaning government and the cash-strapped leftist government of Venezuela, where about 400,000 Portuguese citizens and people of Portuguese origin live. Venezuela is suffering from hyperinflation and shortages of basic goods.

"I told my counterpart that there is a red line for us, and if there is no progress in overcoming this problem there would be consequences for the bilateral relationship," Foreign Minister Augusto Santos Silva said in televised comments.

He called Venezuela's latest crackdown on businesses "an administrative initiative directed against Portuguese interests in Venezuela". The foreign ministry on Friday summoned the Venezuelan ambassador to Lisbon to tell him Portugal was "very preoccupied" with the detentions.

Venezuela President Nicolas Maduro said last week that 34 supermarket managers had been jailed on charges of hiding food and over-charging for it. Local media reported that many of the arrested managers worked at Central Madeirense, a chain founded some 70 years ago by Portuguese immigrants.

Portugal's foreign ministry said there were "various Portuguese nationals and people of Portuguese origin" among the 34 jailed managers.

After the summoning of the ambassador, Arreaza replied in a tweet over the weekend that Venezuela valued its Portuguese community, but the judiciary investigated crimes regardless of the origin of the suspects.

(Reporting by Andrei Khalip, editing by Axel Bugge, editing by Ed Osmond)