New Delhi, India (CNN) -- One of two Taiwanese nationals injured in a shooting at a popular Old Delhi, India, tourist site remained in critical condition Monday after doctors removed a bullet from his abdomen, a hospital official said.
Amit Banerjee, the medical superintendent of the hospital where the two tourists were being treated, added the other tourist is expected to be discharged soon.
Meanwhile, the U.S. and Australian governments have issued safety advisories to their citizens after the shooting on Sunday. And two of India's largest cities -- Delhi and Mumbai -- are on red alert.
Gunmen on a motorcycle fired multiple rounds at a tour bus, Karnail Singh of Delhi police told CNN sister network CNN-IBN on Sunday.
"One of the bullets grazed the head of one tourist, and one has been hit in the stomach," Singh said.
India's tourism minister, Kumari Selja, downplayed Sunday's shooting as a "stray" event aimed at creating panic.
"This attack on tourists shows desperation of those elements who want to create panic in the society by attacking innocent people," Selja said, according to a statement from her ministry. "Investigation agencies are at work" to apprehend the culprits, she said.
India, she insisted, is a safe destination for tourists.
Police, who continue the search for the suspects, said they think the attack is more likely to be the work of a criminal gang than a terror attack.
The attack comes two weeks before the Commonwealth Games, which are expected to draw large crowds to the city. Thousands of athletes from around the world will converge on the city October 3 for the multi-sport event that is held every four years.
"U.S. citizens are urged to always practice good security, maintain a heightened situational awareness and a low profile," the U.S. Embassy posted on its website. "U.S. citizens are advised to monitor local news reports and consider the level of security present when visiting public places, including religious sites."
The message follows a travel alert issued earlier this month about the Commonwealth Games in general:
"The U.S. Mission in India alerts U.S. citizens traveling to or residing in India to safety and security issues related to the 2010 Commonwealth Games scheduled to be held in New Delhi, India, between October 3 and October 14, 2010, especially in light of the worldwide caution issued by the Department of State on August 12, 2010, regarding the continuing threat of terrorist actions and violence against U.S. citizens and interests throughout the world."
Athletes from more than 70 countries in Africa, North and South America, Asia, Europe, the Caribbean island nations and the South Pacific region are expected to take part in the games, which feature such sporting events as basketball, archery, table tennis, squash, badminton, bowling, gymnastics and swimming.
On Monday, Australia warned its citizens in a travel advisory that the event carries a "high risk of terrorism."
"Australians in New Delhi should be aware that the Commonwealth Games will be held in a security environment where there is a high risk of terrorism," the advisory said.
It added that New Delhi has seen at least 14 major terrorist attacks since 2000 in public places, such as markets and train stations.
Police in New Delhi insist Sunday's shooting was not targeted at the games.
"It was a local mischief," police spokesman Rajan Bhagat said Monday.
Security has, however, been stepped up in the Indian capital, he added.
"We assure full security not only for the games but also for the city," Bhagat said.
CNN's Harmeet Shah Singh contributed to this report.