China insists that Taiwan acknowledge the existence of the consensus, under which the two sides notionally agreed that there is "one China" though it is now ruled from different seats of power in Beijing and Taipei, as the foundation of cross-Strait relations.
In the past year Burkina Faso and the Dominican joined China's side, and in previous years Panama and the tiny African state of Sao Tome have also done the same.
Wu said that Taipei had been asked to pay an "enormous sum" for the port project, which he said would only end up leaving both Taiwan and El Salvador in debt.
"We will turn to countries with similar values to fight together against China's increasingly out-of-control global behavior", Tsai said.
In March, US President Donald Trump signed the Taiwan Travel Act - a non-binding bill encouraging the United States to send senior officials to Taiwan to meet Taiwanese counterparts.
Beijing claims Taiwan is an inseparable part of China and will not maintain ties with any country that has formal diplomatic ties with Taiwan.
A file photo shows Tsai with Salvadoran President Salvador Sanchez Ceren during her visit to the nation in January 2017.
"Taiwan will not yield because of pressure", Tsai said in a televised address.
The communique was signed by Chinese State Councilor and Foreign Minister Wang Yi and Salvadorean Foreign Minister Carlos Castaneda.
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This is the first time the current administration announced it was severing diplomatic relations with a formal ally before that ally declared it was switching recognition to Beijing.
In Beijing, Castaneda said it was a strategic decision his government made to "create conditions to change the historical standing of our country and to really elevate the livelihood of our people".
El Salvador has cut its so-called "diplomatic ties" with Taiwan, and it will no longer have any official relations or any official exchanges with Taiwan in any form, he pledged.
"I believe the Salvadorean people will feel the Chinese people's friendship and hospitality and benefit from the two countries' cooperation", Wang said, stressing that history will prove that forging diplomatic relations with China is in the fundamental and long-term interests of the Salvadorean people.
Other than the Holy See, Taipei's remaining diplomatic allies are mostly miniature island nations or developing countries to which Taiwan has to dole out aid to help them stay loyal.
The move comes just a day after China's foreign ministry said it had complained to the USA over Taiwanese President Tsai's visits this month to Los Angeles and Houston while in transit to diplomatic allies Paraguay and Belize.
Relations between China and Taiwan have reached a low under Tsai, who belongs to the Democratic Progressive party, which advocates independence for the island.
Democratic Taiwan is one of China's most sensitive territorial issues and Tsai's U.S. stopovers in the United States, a customary practice for Taiwanese presidents, came amid an increasingly bitter trade war between Beijing and Washington.
The Communist Party government has waged an intense campaign of diplomatic pressure against Tsai's government since she came to power, driven by its ire over her refusal to accept the so-called "1992 consensus" in her inauguration speech. "It would only boost our determination to go overseas", she said on her return to Taiwan on Monday.