WASHINGTON  After coming up short in a first effort, a Democratic lawmaker has again introduced legislation that would roll back a ban on Internet gambling enacted when Republicans led Congress.

The legislation, introduced this month by Representative Barney Frank of Massachusetts, would allow the Treasury Department to license and regulate online gambling companies that serve American customers. Under the current law, approved by Congress in September 2006, financial institutions are banned from handling transactions made to and from Internet gambling sites.

At a news conference announcing the legislation, Mr. Frank, who is chairman of the House Financial Services Committee, pointed out that the federal government could collect increased tax revenues if Internet gambling was regulated. But he said online gambling should be legal as a matter of personal liberty, calling it an activity the government should neither encourage nor prohibit.

“Most actions the government should stay out of,” Mr. Frank said.

Mr. Frank’s bill has roughly two dozen co-sponsors, most of them Democrats. He did not seek the backing of the Obama administration or the leadership in either the House or the Senate.