Seeking to continue recent gains in passenger train ridership, Amtrak this week inaugurated free fares for children 2 through 11.

The National Rail Passenger Corporation, whose losses are subsidized by federal taxpayers, will provide "free kiddie rides" through November 30 from 9 markets, including all stations in the Washington area.

To qualify for the free children's tickets, travel must originate from the selected Amtrak stations but cover any destination across the nation. An official Amtrak "free kiddie ride coupon" must be presented and an adult paying full fare must accompany each child.

Amtrak's coupons were included in advertisements in Tuesday's editions of The Washington Post and in other newspapers for the markets involved - Albany, Seattle, Houston, Dallas, Ft. Worth, Louisville, Nashville and Cincinnati. Each coupon is valid for one free ride for a childf, when accompanied by an adult paying full fare.

Additional children, ages 2 to 11 may travel for the regular one-half fare. Children under 2 will continue to ride free. The only exceptions to the new free fares will be during the following holiday travel periods: July 1, Sept. 25, Oct. 7-10, Oct. 21-24, and Nov. 23-27.

Amtrak's latest promotion is certain to raise new cries of "foul" from the nation's intercity bus companies, who have blamed a recent slide in profitability on Amtrak's increasing patronage and federal subsidies.

Greyhound lines, the largest bus firm, currently offers half-fare rates for children 2 to 11. A nationwide maximum fare for adults of $50 between two cities on Greyhound busses expired yesterday and will be $75, effective today.

In the past several years, more than $1 billion has been appropriated by Congress for Amtrak to buy new equipment and expand its facilities.

Amtrak operated with a loss of $438 million in the year ended September 30. A House appropriations subcommittee recently appropriated $95 million for capital spending and $490 million to subsidize operations for fiscal year 1978, which starts October 1.

Despite the losses, Amtrak's business has been picking up. During the first quarter of 1977, Amtrak trains carried 4.3 million riders compared with 4.1 million in the same period last year, a gain of 5 per cent.

Preliminary data for April indicates a 64 per cent increase over the 1976 period with more than 1 million riders during the month along the northeast corridor alone, compared with 968,000 a year ago.

Because of track repairs and problems with some engines, howver, ontime performance of Amtrak trains has been declining. Of 6,886 trains operated during March, 65 per cent arrived on time compared with 75 per cent a year ago. Metroliners between New York and Washington were on time only 58 per cent of the time compared with 71.5 per cent in March, 1976.