Taiwan's air force scrambled aircraft on Friday as Chinese bombers flew around the self-ruled island, just a few hours after Taiwan vowed not to be cowed having lost another diplomatic ally amid growing Chinese pressure.
Tensions between China and Taiwan hiked with the election of Ms Tsai in 2016, after which five countries cut their ties with Taiwan.
China's foreign ministry said in a brief statement it welcomed Burkina to "join in China-Africa friendly cooperation as soon as possible".
"This isn't dollar diplomacy".
He said China poached another of Taiwan's diplomatic partners because it wanted to vent its anger after Taiwan received backing from the global community, Chen said, citing the support Taiwan received directly and indirectly at the World Health Assembly (WHA) in Geneva this past week.
Tsai has lashed out at China's "crude behaviours" since Burkina Faso broke ties.
"We will not cower at all".
"Taiwan needs to form a broader coalition of willing friends to supplement the support it gets from the USA", said Jonathan Sullivan, director of the China Policy Institute at Nottingham University, although he added the U.S. remains the island's top foreign relations priority because of its influence.
Beijing has also demanded worldwide airlines make it clear that Taiwan, Hong Kong and Macau are all part of China on their websites.
Taiwan's President Tsai Ing-wen, in televised remarks, criticized Beijing for trying to undermine the island's sovereignty, saying those efforts "exposed China's anxiety and lack of confidence". Tsai's ruling Democratic Progressive Party says it wants stable relations with China, but hasn't followed Tsai's predecessor, Ma Ying-jeou, in endorsing the "one China" principle.
China is Africa's largest trade partner, with massive investments in mining, construction and banking, though it has been less active to date in Burkina.
The Vatican is possibly next, as the Holy See and China edge closer to an accord on the appointment of bishops there.
The Chinese government refuses to maintain diplomatic relations with any nation that recognizes Taiwan and has long pressured countries to sever ties with the island.
Some countries have switched back and forth between Beijing and Taipei several times.
The West African country Burkina Faso became the latest country to cut ties with the island.
Burkina Faso had terminated relations with Taipei first in 1973 but restored them in 1994.