In a thinly veiled threat, Ma cited the "increasing voices" within China expecting Beijing to step up its efforts to protect the "one China principle" through a process of "reunification through military force".
Taiwan's army gave a demonstration of its defence capabilities on Wednesday, amid a backdrop of increased tension with mainland China.
But in her first interview since Saturday's re-election, Tsai told the BBC there was no need to formally announce independence because the island already runs itself.
The "one-China principle" is a "universal consensus" held by the worldwide community, he said, and one that will "not be affected in the slightest by a local election in Taiwan".
Despite the result, Chinese officials said on Wednesday that Beijing will not change its policy of annexing Taiwan through its "one country, two systems" framework.
For decades, it was a dictatorship under Chiang Kai-shek's nationalists following their 1949 defeat to the communists in China's civil war.
Taiwan is a sovereign island state off the coast of China.
"We have a separate identity and we're a country of our own", Tsai said. "We're a successful democracy, we have a pretty decent economy, [and] we deserve respect from China".
Tsai, who was re-elected to a second term in a landslide victory over the weekend, told an impromptu press conference at the Presidential Office that she had signed the Anti-Infiltration Act into law earlier on Wednesday, emphasizing that her government is against infiltration, but not against exchanges.
But, China's Taiwan Affairs Office spokesman Ma Xiaoguang was quick to pour cold water on Tsai's proposal, blaming her party for causing a cross-strait stalemate over the past four years.
The U.S. was quick to congratulate Tsai on her election win, with Secretary of State Michael Pompeo calling Taiwan a "model for the Indo-Pacific region and a force for good in the world".
Taiwan's president Tsai Ing-wen has called on China to face reality and review its current policy toward the de facto nation that Beijing claims is part of its territory.
For President Tsai's critics, her stance is needlessly provocative, one that only risks increasing the very danger she warns about - open hostility.
But strong-arm tactics pushed voters to back Tsai's Democratic Progressive Party, driven in part by China's hard-line response to months of huge and sometimes violent protests in favor of democracy in Hong Kong.