Tension between democratic Taiwan and its big neighbour has increased in recent months, with China suspicious the administration of President Tsai Ing-wen wants to push for the island's formal independence.
The two Xian H-6K strategic bombers were on a long-range air exercise and the air force scrambled F-16 fighter jets to observe them, the statement said.
The news agency said the island's foreign minister would hold a briefing Thursday.
Self-ruled Taiwan is claimed by Beijing as Chinese territory, and has become one of China's most sensitive issues and a potential military flashpoint.
The statement released by the Chinese foreign ministry read: "We welcome Burkina Faso's early accession to the Sino-African friendship and cooperation family based on the one-China principle".
"We will no longer be forbearing, and instead become more determined" in seeking worldwide partnerships, Ms. Tsai said, adding that Taiwan wouldn't counter Chinese "dollar diplomacy" with similar tactics. The two sides often use economic support and other aid as bargaining chips for diplomatic recognition. Japanese retailer Muji was fined after being found to be using packaging that listed Taiwan as a country while USA retailer Gap Inc issued an apology last week for selling a T-shirt which it said had an incorrect map of China. The gesture angered Chinese leaders who saw it as a break from the USA practice of lower-level exchanges with Taiwan since Washington switched to recognize China in 1979.
The attack to China from Taiwan continued on Twitter, where the Ministry of Foreign Affairs of the island tweeted: "We ended 24 years of ties with #BurkinaFaso today".
The Chinese have long wanted for the Taiwanese to come under Beijing rules.
The Chinese counterpart of this ministry "welcomed" Burkina Faso's move, leading to think Beiking will soon establish diplomatic relations with the county.
Appeared in the May 25, 2018, print edition as 'Taiwan Loses Ground In Diplomatic Contest'.