President Donald Trump tweeted congratulations to his Chinese counterpart Tuesday morning, acknowledging the 70th anniversary of Community Party rule in China. But several members of Trump's own Republican Party were not in the same congratulatory mood.

"Congratulations to President Xi and the Chinese people on the 70th Anniversary of the People's Republic of China," Trump wrote.

Oct. 1 is China's National Day, the state holiday marking the establishment of the People's Republic of China, but protests flared Tuesday in Hong Kong, overshadowing the holiday. At least 180 protestors were arrested, and a pro-democracy protester was shot in the chest.

Some Republican lawmakers, including Senate Majority Leader Mitch McConnell, later issued statements diverging with Trump's commemoration, though they did not mention Trump.

"On the 70th anniversary of the People’s Republic of China, we should pause to recognize the many millions of lives lost under Chinese communist rule,"McConnell said in a statement.

"I especially condemn the continued use of violence against democratic activists in Hong Kong. It is darkly fitting that on the 70th anniversary of the PRC, its agents would be reduced to using force against protesters in Hong Kong who seek to preserve basic personal freedoms. The CCP has always squashed dissent with force," McConnell wrote.

Hong Kong is a semiautonomous region of China, having been promised "a high degree of autonomy" after its handover from British rule in 1997. Protestors have taken to the streets over the past several months over fears that citizens' civil liberties and political freedoms were being eroded by China's Communist Party.

More:Trump lauds China; police chief laments one of Hong Kong's 'most violent and chaotic days'

Sen. Ted Cruz, R-Texas, slammed the shooting of a protestor as an "unacceptable escalation in the Chinese Communist Party’s assault on the people of Hong Kong and their peaceful protests against tyranny."

House Republican Conference Chair Liz Cheney, R-Wyo., issued a joint statement with Rep. Mike Gallagher, R-Wisc., denouncing the Communist Party.

"This is not a day for celebration. Rather, it is an opportunity to remember the victims, past and present, of the Chinese Communist Party," they wrote, adding that "we rededicate ourselves to ensuring that the Chinese Communist Party is left on the ash heap of history.”

The differing statements highlight the differences between Trump and some Republicans about foreign policy in China.

Trump has generally avoided criticizing the Chinese government over its handling of protests in Hong Kong. Last month, he called the situation in Hong Kong "tough" and "tricky." Congressional Republicans, on the other hand, have urged actions in support of the protestors.

Speaking at the United Nations at the end of April, Trump briefly praised the protestors and said, "we're also carefully monitoring the situation in Hong Kong."

“The world fully expects that the Chinese government will honor its binding treaty made with the British and registered with the United Nations in which China commits to protect Hong Kong's freedom, legal system and democratic ways of life,” Trump said.

Contributing: John Bacon.