U.S. Secretary of State Mike Pompeo said he was gravely concerned over remarks made by Hong Kong's Chief Executive Carrie Lam, in which she warned that the recent pan-democratic primary election may have violated the new security law.

Hong Kong’s pan-democrats support increased democracy and have denounced mainland China’s new overreaching security laws.

“If this so-called primary’s election purpose is to achieve the ultimate goal of…resisting every policy initiative of Hong Kong as their government, then it may fall into the category of subverting the state power -- which is now one of the four types of offenses under the new national security law,” Lam said  in response to the elections.

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The recent primary election had a reported turnout of 600,000 voters, which will select representatives from five different regions to run for Hong Kong’s Legislation Council on Sept. 6, according to the Hong Kong Free Press.

“I warmly congratulate Hong Kong’s pan-democrats for their successful primary election,” Pompeo said Tuesday. “Their enthusiasm clearly demonstrates their desire to make their voices heard in the face of the Chinese Communist Party’s efforts to suffocate the territory’s freedoms.”

In a press conference Monday, Lam said that the primary elections were not a legitimate part of the election system in Hong Kong.

Lam then said that the government received many complaints about the recent elections, and cited law 599G which prohibits “group gatherings of more than 50 people.” She said this was a factor in the investigation the government will now open on this weekend’s primary election.

She also said that the primary election is an "unfairness" to the September 6 election and potentially breached the “privacy commission” -- though she did not expand on how privacy was violated.

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“If we discover there is sufficient evidence to take action, we will take action,” Lam said Monday.

The new security laws have criminalized secession, subversion, terrorism and collusion with foreign forces, with sentences of up to life in prison for those who are found guilty.

Pro-democracy protesters have been arrested for waiving Hong Kong Independence flags and demonstrating against mainland China’s attempts to gain control in the once semi-autonomous region.

The U.S. has implemented policy changes, such as rolling back Hong Kong’s Special Status -- which meant the U.S. recognized Hong Kong as separate from China and allowed for benefits largely through trade and economics, meaning that Hong Kong was not affected by the U.S.-China trade war.

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“We note with grave concern Hong Kong Chief Executive Carrie Lam’s threat that this primary may have violated Beijing’s new ‘national security’ law for the territory, once again demonstrating the Chinese Communist Party’s fear of democracy and its own people’s free thinking,” Pompeo said Tuesday.

“We will be watching developments closely, especially as the September 6 Legislative Council elections draw closer,” Pompeo added.