China's military drills near Taiwan on two consecutive days this week were "completely inappropriate," a U.S. State Department official said on Wednesday.

On Monday, Chinese jets crossed an unofficial middle line in the Taiwan Strait, just a day after Chinese fighters and bombers flew around the island. Both generally stay on their respective sides.

"Absolutely it concerns us" said R. Clarke Cooper, assistant secretary for political-military affairs at the U.S. Department of State.

"It was completely inappropriate of China to take such an aggressive act," Cooper told CNBC's Nancy Hungerford in Singapore.

China claims self-ruled Taiwan as Chinese territory that must one day be reunited with the mainland and Beijing has never renounced the use of force to take Taiwan by force.

Tensions between China and Taiwan have risen since Taiwanese President Tsai Ing-wen from the independence-leaning Democratic Progressive Party took office in 2016. She won re-election in January on a platform of defending Taiwanese sovereignty.

Recently, tensions spiked further as Taipei accused Beijing of blocking Taiwan's access to the World Health Organization amid the outbreak of the COVID-19. This particular strain of coronavirus is believed to have originated from the Chinese city of Wuhan, but has also hit Taiwan.

The U.S. has no formal diplomatic ties with Taiwan but is its main arms supplier.

"All states, including China, are part of the broader constellation in the Indo-Pacific region," said Cooper. "What that means is that there should be responsible behavior to make sure that the region is free and open — not just for navigation but also for trade and for relationships," he said.

"Such coercive, aggressive behavior is counter to having a free and open Indo-Pacific region," he said.

China's People's Liberation Army said on Monday that the drills were aimed at improving combat capabilities.

The U.S. is bound by the Taiwan Relations Act to aid the island's self-defense.

"They need to be able to defend their homeland, and our relationship with Taiwan through the Taiwan Relations Act, we certainly are going do anything we can to bolster their self-defense needs," said Cooper.

Cooper said that China's military moves toward Taiwan this week may be broader reflection of China's stance toward the entire region.

"That aggressive act is not just a reflection on China's relationship with Taiwan, it certainly is reflective about how China may be looking at the entire region in total," said Cooper.