The move has offended some Chinese travelers, who said they might cancel visits to Vietnam, China's state-run news agency Xinhua reported.
Vietnam's passport control offices are refusing to stamp visa pages in the new passports because the map of China inside shows the country's territorial claims on the Paracel Islands, also claimed by Vietnam and Taiwan.
Also claimed by China and Vietnam – as well as the Philippines -- are the Spratly Islands.
Despite the rift, Vietnam is allowing in Chinese tourists with the new passports. Border staff members are issuing Chinese tourists separate visa sheets for insertion into the new passports.
The Chinese public is indignant and may curtail their tourist trips, Xinhua said.
"Ms. Chen, a student at Tsinghua University," said the territorial claims should be printed inside the passports. "The islands originally were ours. It's just like the Diaoyu Islands, we should take back what's ours."
China disputes the Diaoyu Islands with Japan.
"Chen Chuliang, a Beijing resident," said, "If the controversies continue to snowball, I certainly won't choose to go to these countries."
China continually denounces claims to the territories by its neighbors, which actively control most of the disputed islands, the vast majority of which are uninhabited.
Their real value lies in potential mineral, oil, natural gas and fisheries resources.
A Chinese Foreign Ministry spokesman said China soon will make its submission to a U.N. commission concerning the outer limits of its continental shelf beyond 200 nautical miles.
China claims its continental shelf in the East China Sea extends to the Okinawa Trough close to Japan.
A report by the BBC said the Philippines Foreign Ministry is accepting the new Chinese passports while it considers its options.
China's border disputes extend to its hinterland as well, including two Himalayan regions claimed by India.
China's new passports also lay claim to some disputed Himalayan territory and India is stamping its own map on visas issued to Chinese citizens, the BBC reported.
However, border disagreements with India remain low-key, a Xinhua report said, and are mainly talked up by Western media.
"For centuries, the two oriental civilizations were plainly peaceful with each other across the Himalayas," Xinhua said. "Then came the Western colonizers who trickily planted the seeds for territorial disputes between the two countries and even a brief border war in 1962."
The Xinhua article instead focused on increasing economic cooperation between the two countries.
Indian External Affairs Minister Salman Khurshid said the Chinese move was "unacceptable" to India.
But India's Hindustan Times reported that National Security Adviser Shivshankar Menon remained unperturbed by China's passport map that shows Aksai Chin and Arunachal Pradesh areas under Chinese control.
"What has changed?" he said. "Chinese have a view on where the boundary lies. The Chinese chose to put a watermark on their passports which shows the boundaries as they see it. We show our boundary as we see it on visas that we issue."