The Chinese overture came before riots erupted in the capital Port Moresby on January 11, leading to at least 25 deaths, the government said.
China offered last year to help train and equip the South Pacific nation's "policing sector", Foreign Minister Justin Tkatchenko said.
"This offer is being carefully assessed as we do not want to duplicate or compromise agreements already in place with our traditional security partners Australia and the United States," the minister said in a statement.
"It is not going to be the end of the world if we do not come to an understanding or agreement with China," Tkatchenko said.
"Our relationship is one of great respect, and maturity. We are mature enough to know where we stand on different matters."
The United States and its Pacific allies are fending off China's expanding influence in the region, jolted by a secretive security pact Beijing signed with Solomon Islands in 2022.
Papua New Guinea struck separate security agreements with the United States and Australia last year.
The opposition hit out Tuesday at the prospect of Prime Minister James Marape's government signing any "secret" security pact with China.
- 'Lack of control' -
"The terrible Port Moresby riots in mid-January are testament to the division and lack of control and discipline now rampant in the PNG police service," said opposition figure Peter O'Neill, the country's former prime minister.
Papua New Guinea had "rightfully stuck to Australia" for domestic and regional security, he added.
The Port Moresby riots broke out when members of the over-stretched police force went on strike, walking off the job after their pay was mistakenly docked without explanation.
The government would later allege that "rogue" police played a key role in stoking the turmoil. Disgruntled citizens also joined the fray.
Australia's Prime Minister Anthony Albanese said his country remained the "security partner of choice" for Papua New Guinea.
"We're family and we'll continue to engage," he told reporters in Townsville, Queensland.
Papua New Guinea's prime minister is due to visit Australia and address parliament on February 8, Albanese said.
Papua New Guinea is blessed with vast deposits of gold, gas and minerals, luring investors from around the world including China.
It is also plagued by entrenched inequality; about 40 percent of the population is thought to live in extreme poverty.
Australia hammered out a security deal with Papua New Guinea in December last year, including a promise of more police training.
Earlier in the year, Papua New Guinea had granted the United States "unimpeded" access to key naval bases, ports and airfields, sparking criticism that it had yielded too much influence to a foreign power.
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