Reuters reports the INS Kolkata guided missile destroyer and INS Sahyadri frigate will stay in Port Moresby for two days, an Indian embassy official said.
The visit will "enhance maritime cooperation and security in the region", an embassy statement added. India currently holds the rotating presidency of the G20.
The ships will then join naval exercises in Australia as part of the Quadrilateral Security Dialogue, or Quad, a group that also includes Japan and the United States. The Malabar exercise begins next Friday.
The United States and its allies are seeking to deter Pacific island nations from forming security ties with China, a rising concern amid tension over Taiwan, and after Beijing signed a security pact with Solomon Islands. PNG struck a defence agreement with Washington in May.
Pacific island leaders, whose territories span 40 million square km of ocean, have said rising sea levels caused by climate change are their most pressing security priority.
The navy port call follows a visit by Indian Prime Minister Narendra Modi in May to Papua New Guinea. Modi took part in a summit meeting of Pacific nations.
The leaders of both France and Indonesia, as well as senior US and British officials, have also visited PNG in quick succession. US President Joe Biden was forced to cancel a visit because of debt ceiling negotiations in Washington.
Solomon Islands Prime Minister Manasseh Sogavare, who visited Beijing in July, last week broke ground on a China-financed project to build 161 Huawei telecommunications towers across an archipelago with a population of 700,000.
"We will not be deterred by misinformation such as debt traps," he said, according to a government statement.
Michael Green, CEO of the United States Studies Centre at the University of Sydney, said it was not the first time the Pacific Islands have come to world attention during major transitions in international relations.
At the end of the First World War, the islands "consumed attention" at the 1921-22 Washington Naval Treaties amid concern over Japan's access to an undersea cable, said Green, a former senior US national security adviser.
After the Second World War, the US was "determined to keep the former Japanese islands out of the Communist bloc because they were critical to protecting the southern flank below Japan and above Australia," he said. With China's rise, Pacific Islands airfields and undersea cables have again come into play, he added.
China is PNG's largest trading partner. The director of the Pacific Islands Program at the Lowy Institute think-tank, Meg Keen, said the recent push by China into security has "raised concern among Western countries with strong national interests in the region".
"The US is trying to secure a bilateral security agreement with PNG and show it is in the region to stay and will make a positive difference. To date its engagements have been modest," she said.
Pacific Island nations have welcomed the additional interest from the West but will continue to engage with China, she said.
"The Pacific will want more than Pacific frequent flyers, they want genuine partnerships that deliver results," she added.