The protests forced the authorities to shut down the airport in the eastern Indian city of Kolkata, while police beat agitating workers with batons to keep them from storming the terminal in Mumbai.
In New Delhi and Mumbai, workers shouted anti-government slogans as they launched a sit-in protest outside the entrances to the main terminals.
"Unless and until the government heeds our demand to withdraw its decision to privatise Mumbai and Delhi airports, we will not stop our agitation," said Pramod Sharma, a union secretary, the Press Trust of India reported.
"We are ready to go to the extent of even sacrificing our lives."
After a day of protests, the airport in Kolkata, one of India's largest cities, was ordered shut when fire brigade personnel and workers in charge of lighting at the runway joined the protests, the Press Trust of India news agency reported.
The airport decided it could not operate without these vital services and airport management was holding an emergency meeting, the report said. At least one flight was diverted from Kolkata.
Meanwhile, the Mumbai domestic terminal lost all electric power for some 20 minutes before it was restored, an airport official said. No flights were disrupted during the failure.
The protests gathered momentum after the government announced on Tuesday that construction firm, GMR Industries, based in southern Hyderabad and partnered by Germany's Fraport, had won a bid to privatise Delhi airport.
India's GVK group and the South African Airport authority won the bid to privatise Mumbai airport.
Plans to privatise Delhi and Mumbai airports had been stalled for years amid opposition by workers fearing job losses; but both consortiums have promised to absorb 60% of the workforce after three years with AAI to absorb the rest.
"We are ready to go to the extent of even sacrificing our lives"
A leader of the striking workers
Both airports are notorious for their lack of passenger amenities, congested operating conditions and scant duty-free shopping or entertainment for transit passengers. Another 20 to 30 smaller airports are expected to be modernised.
Sharma said the employees were not against plans to upgrade the airports.
"We are only opposing handing over the process to private players. The Airport Authority of India is fully capable to do that," he said.
Union officials in Mumbai said about 3000 staff had walked out from domestic and international airports at 10.30am (0500 GMT) but they did not include traffic controllers or pilots.
"Everything at the airport is normal. The only difference is that instead of using aero bridges they are using stepladders," said Air India spokesman Jitender Bhargava of passengers entering planes.
In Delhi, AAI spokesman Prem Nath said contingency measures were in place to ensure "all services, both air and ground, remain normal and all the facilities for passengers are unaffected".
Late on Tuesday, a government official said the Indian Air Force was on standby to handle air traffic control if the employees did not turn up for work.
About 19 million domestic passengers passed through India's airports in 2005. Analysts predict annual growth of 20% over the next five years as rising incomes and lower fares make air travel more affordable.